Finite Group Databasebeta

← Group #72323211

Character table — Group #72323211

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112
size11222222244444444448888888888888161616161616161616163232323232323232323232323232323232323232323232323232323232323232323232323232646464646464646464646464646464646464646464646464128128128128128128128128
order1222222222222222222222222222224422244444442222244444444444444444444444444444444444444444444444444444444444448888
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-111-1-1-1-11-11111-1-1-1-111-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-11-111-1-1-1-11-1-1-1-1-11111-1-11111-1-1
χ5111111111111111111111111111111111111111111-11-111-11-111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-11-1-111-1-1-111111-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111111111111111111-11-1-1-1-11-1-1-1-1-111-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-11-1-111-1-1-11-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111111111111111-1-1111-1-1111-1-1-1-1111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111111111111111-1-11-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111111111111111111111111111-1-1-1-1111-11111-1111111-1-11111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ101111111111111111111111111111111111111-1-1-1-1111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111111111-1-111-1-111
χ111111111111111111111111111111111111111-1-1-1-111-11111-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-11-1-111-1-1-11-1-1-1-111111111-1-1-1-1
χ121111111111111111111111111111111111111-1-1-1-111-11-1-11-11-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111-11-1-111-1-1-111111-1-1-1-1-1-1-1-11111
χ131111111111111111111111111111111111111-1-1-1-11-11111-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11-1-1-1-1-11111-1-1-1-11111
χ141111111111111111111111111111111111111-1-1-1-11-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111-111-1-1-1-11-11111-1-1-1-11111-1-1-1-1
χ151111111111111111111111111111111111111-1-1-1-11-1-1-111-1-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ161111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-111-1-1
χ1722222222222222222222222222-2-222-2-2-2-2-2-2-22222-200200002000000220000-2-2-2-2000000002222220000-2-2000000-2-2000000000000000000
χ1822222222222222222222222222-2-222-2-2-2-2-2-2-22222-200-20000-2000000-2-20000-2-2-2-20000000022-2-2-2-200002200000022000000000000000000
χ1922222222222222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-200200002000000220000222200000000-2-2-2-2-2-20000-2-200000022000000000000000000
χ2022222222222222222222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-200-20000-2000000-2-20000222200000000-2-22222000022000000-2-2000000000000000000
χ2122222222222222-22-2-2-2222-2-2-2-222-2-2-2-2222-2-22i2i−2i−2i-2000000000000000000002i2i−2i−2i000000002i−2i00000000000000000000000000002-200002i−2i
χ2222222222222222-22-2-2-2222-2-2-2-222-2-2-2-2222-2-22i2i−2i−2i-2000000000000000000002i2i−2i−2i000000002i−2i0000000000000000000000000000-220000−2i2i
χ2322222222222222-22-2-2-2222-2-2-2-222-2-2-2-2222-2-2−2i−2i2i2i-200000000000000000000−2i−2i2i2i00000000−2i2i00000000000000000000000000002-20000−2i2i
χ2422222222222222-22-2-2-2222-2-2-2-222-2-2-2-2222-2-2−2i−2i2i2i-200000000000000000000−2i−2i2i2i00000000−2i2i0000000000000000000000000000-2200002i−2i
χ2522222222222222-22-2-2-2222-2-2-2-2-2-2-2-222-2-2-2222i2i−2i−2i200000000000000000000−2i−2i2i2i000000002i−2i0000000000000000000000000000002i−2i2-200
χ2622222222222222-22-2-2-2222-2-2-2-2-2-2-2-222-2-2-2222i2i−2i−2i200000000000000000000−2i−2i2i2i000000002i−2i000000000000000000000000000000−2i2i-2200
χ2722222222222222-22-2-2-2222-2-2-2-2-2-2-2-222-2-2-222−2i−2i2i2i2000000000000000000002i2i−2i−2i00000000−2i2i0000000000000000000000000000002i−2i-2200
χ2822222222222222-22-2-2-2222-2-2-2-2-2-2-2-222-2-2-222−2i−2i2i2i2000000000000000000002i2i−2i−2i00000000−2i2i000000000000000000000000000000−2i2i2-200
χ2922222222222-2-2-22-22222-2-22-2-2-2222-2-2-22-2-22-2222222000020000-2-2000000002-22-200000000-2-200002-20000-202-20000200000000000000000
χ3022222222222-2-2-22-22222-2-22-2-2-2222-2-2-22-2-22-222222-20000-2000022000000002-22-200000000-2-20000-22000020-220000-200000000000000000
χ3122222222222-2-2-22-22222-2-22-2-2-2222-2-2-22-2-22-2-2-2-2-222000020000-2-200000000-22-22000000002200002-2000020-220000-200000000000000000
χ3222222222222-2-2-22-22222-2-22-2-2-2222-2-2-22-2-22-2-2-2-2-22-20000-200002200000000-22-2200000000220000-220000-202-20000200000000000000000
χ3322222222222-2-2-22-22222-2-22-2-2-2-2-22-222-222-222222-2020000200000-2-2000000-22-2200000000-2-20000002-2000-2002-200020000000000000000
χ3422222222222-2-2-22-22222-2-22-2-2-2-2-22-222-222-222222-20-20000-20000022000000-22-2200000000-2-2000000-22000200-22000-20000000000000000
χ3522222222222-2-2-22-22222-2-22-2-2-2-2-22-222-222-22-2-2-2-2-2020000200000-2-20000002-22-200000000220000002-2000200-22000-20000000000000000
χ3622222222222-2-2-22-22222-2-22-2-2-2-2-22-222-222-22-2-2-2-2-20-20000-200000220000002-22-20000000022000000-22000-2002-200020000000000000000
χ3722222222222-2-2-2-2-2-2-2-22-2-2-222222-22222-2-2-222i2i−2i−2i-20002200022000000-2-2-2-22i−2i−2i2i00000000−2i2i000000000000000000002i2i−2i−2i000000000000
χ3822222222222-2-2-2-2-2-2-2-22-2-2-222222-22222-2-2-222i2i−2i−2i-2000-2-2000-2-200000022222i−2i−2i2i00000000−2i2i00000000000000000000−2i−2i2i2i000000000000
χ3922222222222-2-2-2-2-2-2-2-22-2-2-222222-22222-2-2-22−2i−2i2i2i-20002200022000000-2-2-2-2−2i2i2i−2i000000002i−2i00000000000000000000−2i−2i2i2i000000000000
χ4022222222222-2-2-2-2-2-2-2-22-2-2-222222-22222-2-2-22−2i−2i2i2i-2000-2-2000-2-20000002222−2i2i2i−2i000000002i−2i000000000000000000002i2i−2i−2i000000000000
χ4122222222222-2-2-2-2-2-2-2-22-2-2-2222-2-2-22-2-2-2222-22i2i−2i−2i200000000000000000000−2i2i2i−2i2i2i2i2i−2i−2i−2i−2i−2i2i00000000000000000000000022-2-200000000
χ4222222222222-2-2-2-2-2-2-2-22-2-2-2222-2-2-22-2-2-2222-22i2i−2i−2i200000000000000000000−2i2i2i−2i−2i−2i−2i−2i2i2i2i2i−2i2i000000000000000000000000-2-22200000000
χ4322222222222-2-2-2-2-2-2-2-22-2-2-2222-2-2-22-2-2-2222-2−2i−2i2i2i2000000000000000000002i−2i−2i2i2i2i2i2i−2i−2i−2i−2i2i−2i000000000000000000000000-2-22200000000
χ4422222222222-2-2-2-2-2-2-2-22-2-2-2222-2-2-22-2-2-2222-2−2i−2i2i2i2000000000000000000002i−2i−2i2i−2i−2i−2i−2i2i2i2i2i2i−2i00000000000000000000000022-2-200000000
χ45222222222-2-222-22-2222-22-2-22-2-222-22-2-2-2-22220000-22020020200-2-200-2-20000000000000000000000-22002-20200-2-200020000000000000000
χ46222222222-2-222-22-2222-22-2-22-2-222-22-2-2-2-22220000-220-20020-200-2-200220000000000000000000000-2200-220-20022000-20000000000000000
χ47222222222-2-222-22-2222-22-2-22-2-222-22-2-2-2-22220000-2-20200-202002200-2-200000000000000000000002-2002-20-20022000-20000000000000000
χ48222222222-2-222-22-2222-22-2-22-2-222-22-2-2-2-22220000-2-20-200-20-20022002200000000000000000000002-200-220200-2-200020000000000000000
χ49222222222-2-222-22-2222-22-2-22-2-2-2-2-222222-2-2-200002022000220000-2-2-2-2000000000000000000000000-22-2220-2-20000200000000000000000
χ50222222222-2-222-22-2222-22-2-22-2-2-2-2-222222-2-2-20000202-20002-20000-2-222000000000000000000000000-222-2-20220000-200000000000000000
χ51222222222-2-222-22-2222-22-2-22-2-2-2-2-222222-2-2-2000020-22000-22000022-2-20000000000000000000000002-2-22-20220000-200000000000000000
χ52222222222-2-222-22-2222-22-2-22-2-2-2-2-222222-2-2-2000020-2-2000-2-2000022220000000000000000000000002-22-220-2-20000200000000000000000
χ53222222222-2-2-2-2222222-2-22-2-22222-2-222-22-22-20000-2220002200022220000000000000000000022-2-2-2-2-2-2000000002-2000000000000000000
χ54222222222-2-2-2-2222222-2-22-2-22222-2-222-22-22-20000-22-20002-200022-2-200000000000000000000-2-222-2-22200000000-22000000000000000000
χ55222222222-2-2-2-2222222-2-22-2-22222-2-222-22-22-20000-2-22000-22000-2-22200000000000000000000-2-22222-2-200000000-22000000000000000000
χ56222222222-2-2-2-2222222-2-22-2-22222-2-222-22-22-20000-2-2-2000-2-2000-2-2-2-20000000000000000000022-2-22222000000002-2000000000000000000
χ57222222222-2-2-2-2222222-2-22-2-222-2-2-2-2-2-22-22-2200002000000000000000000000000000000000022-2-2000000222-22-2-22-2-20000000000000000
χ58222222222-2-2-2-2222222-2-22-2-222-2-2-2-2-2-22-22-2200002000000000000000000000000000000000022-2-2000000-2-2-22-22-22220000000000000000
χ59222222222-2-2-2-2222222-2-22-2-222-2-2-2-2-2-22-22-22000020000000000000000000000000000000000-2-2220000002-22-2-222-2-220000000000000000
χ60222222222-2-2-2-2222222-2-22-2-222-2-2-2-2-2-22-22-22000020000000000000000000000000000000000-2-222000000-22-222-22-22-20000000000000000
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χ62444444444-4-444-4-4-4-4-4-4-44-44-444-4-44-4-4-444-4440000-40000000000000000000000000000000000000000000000000000000000000000000000
χ63444444444-4-4-4-44-44-4-4-4-4-4444-4-44444-4-4-44-4-44000040000000000000000000000000000000000000000000000000000000000000000000000
χ64444444444-4-4-4-44-44-4-4-4-4-4444-4-4-4-444444-444-40000-40000000000000000000000000000000000000000000000000000000000000000000000
χ65444-4-44-4-4444000404-4-4-400400000-4000000004i−4i4i−4i000022000-2-200000022-2-200000000000000000000000000000000002i−2i2i−2i000000000000
χ66444-4-44-4-4444000404-4-4-400400000-4000000004i−4i4i−4i0000-2-200022000000-2-2220000000000000000000000000000000000−2i2i−2i2i000000000000
χ67444-4-44-4-4444000404-4-4-400400000-400000000−4i4i−4i4i000022000-2-200000022-2-20000000000000000000000000000000000−2i2i−2i2i000000000000
χ68444-4-44-4-4444000404-4-4-400400000-400000000−4i4i−4i4i0000-2-200022000000-2-22200000000000000000000000000000000002i−2i2i−2i000000000000
χ69444-4-44-4-4444000-40-444-400-4000004000000004-4-44000022000-2-2000000-2-22200000000000000000000000000000000002-2-22000000000000
χ70444-4-44-4-4444000-40-444-400-4000004000000004-4-440000-2-20002200000022-2-20000000000000000000000000000000000-222-2000000000000
χ71444-4-44-4-4444000-40-444-400-400000400000000-444-4000022000-2-2000000-2-2220000000000000000000000000000000000-222-2000000000000
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χ7544-444-4-4-4400004-444-4400-4004-40000000000000000000-22000-22000000-22-22000022-2-222-2-200-440000000000000000000000000000000000
χ7644-444-4-4-4400004-444-4400-4004-40000000000000000000-22000-22000000-22-220000-2-222-2-222004-40000000000000000000000000000000000
χ7744-444-4-4-440000-44-4-44-4004004-400000000000000000002-20002-2000000-22-2200002i2i−2i−2i−2i−2i2i2i00004i−4i00000000000000000000000000000000
χ7844-444-4-4-440000-44-4-44-4004004-400000000000000000002-20002-2000000-22-220000−2i−2i2i2i2i2i−2i−2i0000−4i4i00000000000000000000000000000000
χ7944-444-4-4-440000-44-4-44-4004004-40000000000000000000-22000-220000002-22-200002i2i−2i−2i−2i−2i2i2i0000−4i4i00000000000000000000000000000000
χ8044-444-4-4-440000-44-4-44-4004004-40000000000000000000-22000-220000002-22-20000−2i−2i2i2i2i2i−2i−2i00004i−4i00000000000000000000000000000000
χ8144-4-4-4-44440044040-4-440-400-40000040000000000000042-200-4-22000000-222-2000000000000000000000000000000000000002-22-200000000
χ8244-4-4-4-44440044040-4-440-400-4000004000000000000004-2200-42-20000002-2-2200000000000000000000000000000000000000-22-2200000000
χ8344-4-4-4-44440044040-4-440-400-400000400000000000000-42-2004-22000000-222-200000000000000000000000000000000000000-22-2200000000
χ8444-4-4-4-44440044040-4-440-400-400000400000000000000-4-220042-20000002-2-22000000000000000000000000000000000000002-22-200000000
χ8544-4-4-4-444400-4-40-4044-40400-40000040000000000000002-2000-2200004-42-2-22000000000000000000000000000000000000002-2-2200000000
χ8644-4-4-4-444400-4-40-4044-40400-40000040000000000000002-2000-220000-442-2-2200000000000000000000000000000000000000-222-200000000
χ8744-4-4-4-444400-4-40-4044-40400-4000004000000000000000-220002-200004-4-222-200000000000000000000000000000000000000-222-200000000
χ8844-4-4-4-444400-4-40-4044-40400-4000004000000000000000-220002-20000-44-222-2000000000000000000000000000000000000002-2-2200000000
χ89888-8-88-8-88-8-8000808-8-8800-800000800000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ90888-8-88-8-88-8-8000-80-888800800000-800000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9188-888-8-8-880000888-88-800-800-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9288-888-8-8-880000-8-8-88-8800800-8800000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9388-88-888-8-80000000000000000000008-8000000000040000-400004-40000000000000000000000000000000000000000000000000000000000
χ9488-88-888-8-80000000000000000000008-80000000000-4000040000-440000000000000000000000000000000000000000000000000000000000
χ9588-88-888-8-8000000000000000000000-88000000000040000-40000-440000000000000000000000000000000000000000000000000000000000
χ9688-88-888-8-8000000000000000000000-880000000000-40000400004-40000000000000000000000000000000000000000000000000000000000
χ9788-8-888-88-8000000000000000008-800000000000000040000-4000004-400000000000000000000000000000000000000000000000000000000
χ9888-8-888-88-8000000000000000008-8000000000000000-40000400000-4400000000000000000000000000000000000000000000000000000000
χ9988-8-888-88-800000000000000000-8800000000000000040000-400000-4400000000000000000000000000000000000000000000000000000000
χ10088-8-888-88-800000000000000000-88000000000000000-400004000004-400000000000000000000000000000000000000000000000000000000
χ10188-8-8-8-888800880-8088-80-800800000-80000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-8-888800-8-8080-8-880800800000-80000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10316161616-16-16-1616-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ104161616-1616-1616-16-160000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ10516-1600000008-88-880-800000000000000000000000000000000000000000000000000004i−4i004i−4i00000000000000000000000000000000000000
χ10616-1600000008-88-880-80000000000000000000000000000000000000000000000000000−4i4i00−4i4i00000000000000000000000000000000000000
χ10716-1600000008-8-88-80800000000000000000000000000000000000000000000000000004-400-4400000000000000000000000000000000000000
χ10816-1600000008-8-88-8080000000000000000000000000000000000000000000000000000-44004-400000000000000000000000000000000000000
χ10916-160000000-888-8-808000000000000000000000000000000000000000000000000004-4004-40000000000000000000000000000000000000000
χ11016-160000000-888-8-80800000000000000000000000000000000000000000000000000-4400-440000000000000000000000000000000000000000
χ11116-160000000-88-8880-8000000000000000000000000000000000000000000000000004i−4i00−4i4i0000000000000000000000000000000000000000
χ11216-160000000-88-8880-800000000000000000000000000000000000000000000000000−4i4i004i−4i0000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).