Finite Group Databasebeta

← Group #72324324

Character table — Group #72324324

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222224488888888888888888888888888888888816161616161616161616161616161616161616161616161616163232323232323232323232323232646464646464128128128128
order12222222222222222222244444444444444444444444422222444444444444444444444244444444444444488884888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-111-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111111-1-111-1-1-1-111-1-1
χ4111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1-1-11111-1-111
χ511111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-11-1-111111-1-1-1-1-1-111
χ611111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-11-1-1111-1-1111111-1-1
χ711111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1-1-11111111111111111-1-1111-1-11-1-11-1-1111111-1-1-1-1
χ811111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-11111
χ91111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11111-1-1-1-111-1-111111-111111-1-1-1-11-1-1-111-1-11-11-1
χ101111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111111-1-11111-1-1-1-111-1-1111-11-1-1-1-111-1-1-1-11-111-1-111-11-11
χ111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-11111-1-1111111-1111111-1-1-1-1-11-1-1-1-1111-1-11
χ121111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1111-1-111-1-1-1-11111-1-111111-1-11-1-1-111-1-1-1-1-111111-1-1-111-1
χ131111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-1-11111-1-11111111-1111-1-1-111-11-1-1-1-1-111-111-1
χ141111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-1-11111-1-111111-11-1-1-1-1-1-1-111-11-11111-1-11-1-11
χ151111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-111-1-11111-11111-1-1-111-1-11-1-111-1-1-11-11
χ161111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-111-1-1111-1-11-1-1-1-1-1-111-1-1111-1-1111-11-1
χ172222222222222222200002200000000000022222222222200-2000000-2-2-2-2-2-2-2-22222-2-2-200000000-200-2000000000000
χ1822222222222222222000022000000000000-2-2-2-2-2-2-2-2222200-200000022222222-2-2-2-2-2-2-200000000-200-2000000000000
χ19222222222222222220000-2-200002222222200000000-2-2-2-200-200222200000000000022-20-2-200000-2002-2-20000000000
χ20222222222222222220000-2-20000-2-2-2-2-2-2-2-200000000-2-2-2-200-200-2-2-2-200000000000022-202200000-2002220000000000
χ21222222222222222222222-2-222220000000000000000-2-2-2-2222220000000000000000-2-22000000-2-22-2-2-2000000000000
χ2222222222222222222-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-22-2-20000000000000000-2-2200000022222-2000000000000
χ232222222222222-2-2-2-20000220000000000002222-2-2-2-222-2-200-2000000-2-2-2-2222222-2-2-2-2-2000000002002000000000000
χ242222222222222-2-2-2-2000022000000000000-2-2-2-2222222-2-200-20000002222-2-2-2-2-2-222-2-2-2000000002002000000000000
χ252222222222222-2-2-2-20000-2-200002222-2-2-2-200000000-2-22200-20022-2-200000000000022-20-2200000200-2-220000000000
χ262222222222222-2-2-2-20000-2-20000-2-2-2-2222200000000-2-22200-200-2-22200000000000022-202-200000200-22-20000000000
χ272222222222222-2-2-2-22222-2-2-2-2-2-20000000000000000-2-222-2-22220000000000000000-2-22000000-2-2-2222000000000000
χ282222222222222-2-2-2-2-2-2-2-2-2-222220000000000000000-2-222222-2-20000000000000000-2-2200000022-2-2-22000000000000
χ292222222222-2-2-2000000002-2222200002222222200002-200-2-2-20000-2-222-2-20000-2-2002-220020000002-200-20000000000
χ302222222222-2-2-2000000002-222220000-2-2-2-2-2-2-2-200002-200-2-2-2000022-2-222000022002-2200-20000002-20020000000000
χ312222222222-2-2-2000000002-2-2-2-2-200002222-2-2-2-200002-20022-20000-2-2-2-222000022002-22002000000-2200-20000000000
χ322222222222-2-2-2000000002-2-2-2-2-20000-2-2-2-2222200002-20022-200002222-2-20000-2-2002-2200-2000000-220020000000000
χ332222222222-2-2-200000000-2222222222000000002222-2200-2-2-200-2-200000022-2-200-2-2-222020000000-220-200000000000
χ342222222222-2-2-200000000-222222-2-2-2-200000000-2-2-2-2-2200-2-2-20022000000-2-2220022-2220-20000000-220200000000000
χ352222222222-2-2-200000000-22-2-2-2-2222200000000-2-2-2-2-220022-200-2-2000000-2-2220022-2220200000002-20-200000000000
χ362222222222-2-2-200000000-22-2-2-2-2-2-2-2-2000000002222-220022-2002200000022-2-200-2-2-2220-200000002-20200000000000
χ372222222222-2-2-2000022222-2000022220000222200002-200002-2-2-2-200-2-2220000-2-200-22-20-200002-20000200000000000
χ382222222222-2-2-2000022222-20000-2-2-2-20000-2-2-2-200002-200002-2-2220022-2-200002200-22-20200002-20000-200000000000
χ392222222222-2-2-200002222-2200000000222200002222-2200002-2-200-2-20000-2-22200-2-22-2-200-2000-220000020000000000
χ402222222222-2-2-200002222-2200000000-2-2-2-20000-2-2-2-2-2200002-2-20022000022-2-200222-2-2002000-2200000-20000000000
χ412222222222-2-2-20000-2-2-2-22-2000022220000-2-2-2-200002-20000222-2-20022-2-200002200-22-20-20000-220000200000000000
χ422222222222-2-2-20000-2-2-2-22-20000-2-2-2-20000222200002-200002222200-2-2220000-2-200-22-2020000-220000-200000000000
χ432222222222-2-2-20000-2-2-2-2-220000000022220000-2-2-2-2-22000022200-2-2000022-2-200222-2-200-20002-20000020000000000
χ442222222222-2-2-20000-2-2-2-2-2200000000-2-2-2-200002222-22000022200220000-2-22200-2-22-2-20020002-200000-20000000000
χ4544444-4-44-4-4000000000000400000000000000004i4i−4i−4i0-4000000000000000000000000002002-2-20000000000002i−2i0000
χ4644444-4-44-4-4000000000000400000000000000004i4i−4i−4i0-400000000000000000000000000-200-222000000000000−2i2i0000
χ4744444-4-44-4-400000000000040000000000000000−4i−4i4i4i0-4000000000000000000000000002002-2-2000000000000−2i2i0000
χ4844444-4-44-4-400000000000040000000000000000−4i−4i4i4i0-400000000000000000000000000-200-2220000000000002i−2i0000
χ494444-44-4-44-400000000000400000000000004i4i−4i−4i0000-4000000000000000000000000000200-22-200000000002i−2i000000
χ504444-44-4-44-400000000000400000000000004i4i−4i−4i0000-4000000000000000000000000000-2002-220000000000−2i2i000000
χ514444-44-4-44-40000000000040000000000000−4i−4i4i4i0000-4000000000000000000000000000200-22-20000000000−2i2i000000
χ524444-44-4-44-40000000000040000000000000−4i−4i4i4i0000-4000000000000000000000000000-2002-2200000000002i−2i000000
χ534444-4-44-4-4444-444-4-4000000000000000000000000000000000000000000000000000000200-2-22000000002-200000000
χ544444-4-44-4-4444-444-4-4000000000000000000000000000000000000000000000000000000-20022-200000000-2200000000
χ554444-4-44-4-4444-4-4-444000000000000000000000000000000000000000000000000000000200-2-2200000000-2200000000
χ564444-4-44-4-4444-4-4-444000000000000000000000000000000000000000000000000000000-20022-2000000002-200000000
χ5744-4-400400-44-40004-422-2-20022-2-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i00002-202-22i−2i2i−2i000000002i−2i2i−2i000000000000000000000000000
χ5844-4-400400-44-40004-422-2-20022-2-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i00002-202-2−2i2i−2i2i00000000−2i2i−2i2i000000000000000000000000000
χ5944-4-400400-44-40004-4-2-22200-2-2222i2i−2i−2i2i2i−2i−2i−2i2i−2i2i−2i2i−2i2i0000-220-222i−2i2i−2i00000000−2i2i−2i2i000000000000000000000000000
χ6044-4-400400-44-40004-4-2-22200-2-222−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i0000-220-22−2i2i−2i2i000000002i−2i2i−2i000000000000000000000000000
χ6144-4-400400-44-4000-4422-2-200-2-2222i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i0000-2202-22i−2i−2i2i000000002i−2i−2i2i000000000000000000000000000
χ6244-4-400400-44-4000-4422-2-200-2-222−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i0000-2202-2−2i2i2i−2i00000000−2i2i2i−2i000000000000000000000000000
χ6344-4-400400-44-4000-44-2-2220022-2-22i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i00002-20-222i−2i−2i2i00000000−2i2i2i−2i000000000000000000000000000
χ6444-4-400400-44-4000-44-2-2220022-2-2−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i00002-20-22−2i2i2i−2i000000002i−2i−2i2i000000000000000000000000000
χ6544-4-400400-4-4404-40022-2-20022-2-22i2i−2i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2i−2i0000-220-22−2i2i−2i2i00000000−2i2i−2i2i000000000000000000000000000
χ6644-4-400400-4-4404-40022-2-20022-2-2−2i−2i2i2i−2i−2i2i2i−2i2i−2i2i−2i2i−2i2i0000-220-222i−2i2i−2i000000002i−2i2i−2i000000000000000000000000000
χ6744-4-400400-4-4404-400-2-22200-2-2222i2i−2i−2i2i2i−2i−2i−2i2i−2i2i−2i2i−2i2i00002-202-2−2i2i−2i2i000000002i−2i2i−2i000000000000000000000000000
χ6844-4-400400-4-4404-400-2-22200-2-222−2i−2i2i2i−2i−2i2i2i2i−2i2i−2i2i−2i2i−2i00002-202-22i−2i2i−2i00000000−2i2i−2i2i000000000000000000000000000
χ6944-4-400400-4-440-440022-2-200-2-2222i2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i00002-20-22−2i2i2i−2i00000000−2i2i2i−2i000000000000000000000000000
χ7044-4-400400-4-440-440022-2-200-2-222−2i−2i2i2i2i2i−2i−2i−2i2i−2i2i2i−2i2i−2i00002-20-222i−2i−2i2i000000002i−2i−2i2i000000000000000000000000000
χ7144-4-400400-4-440-4400-2-2220022-2-22i2i−2i−2i−2i−2i2i2i−2i2i−2i2i2i−2i2i−2i0000-2202-2−2i2i2i−2i000000002i−2i−2i2i000000000000000000000000000
χ7244-4-400400-4-440-4400-2-2220022-2-2−2i−2i2i2i2i2i−2i−2i2i−2i2i−2i−2i2i−2i2i0000-2202-22i−2i−2i2i00000000−2i2i2i−2i000000000000000000000000000
χ7388888-8-88-8-8000000000000-8000000000000000000000800000000000000000000000000000000000000000000000000
χ748888-88-8-88-800000000000-80000000000000000000008000000000000000000000000000000000000000000000000000
χ758888-8-88-8-88-8-880000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ7688-8-800-800800000000000000000000000004-4-444-4-44004-4000000000000000000000000000000000000000000000000
χ7788-8-800-800800000000000000000000000004-4-44-444-400-44000000000000000000000000000000000000000000000000
χ7888-8-800-80080000000000000000000000000-444-44-4-4400-44000000000000000000000000000000000000000000000000
χ7988-8-800-80080000000000000000000000000-444-4-444-4004-4000000000000000000000000000000000000000000000000
χ808-88-80800-8000000000000004-44-400004i−4i4i−4i0000000000000000000004i−4i0000000000000000000000000000000000000
χ818-88-80800-8000000000000004-44-40000−4i4i−4i4i000000000000000000000−4i4i0000000000000000000000000000000000000
χ828-88-80800-800000000000000-44-4400004i−4i4i−4i000000000000000000000−4i4i0000000000000000000000000000000000000
χ838-88-80800-800000000000000-44-440000−4i4i−4i4i0000000000000000000004i−4i0000000000000000000000000000000000000
χ848-88-80-8008000000004-44-40000004-44-40000000000000000000000000004-400000000000000000000000000000000000
χ858-88-80-8008000000004-44-4000000-44-44000000000000000000000000000-4400000000000000000000000000000000000
χ868-88-80-800800000000-44-440000004-44-4000000000000000000000000000-4400000000000000000000000000000000000
χ878-88-80-800800000000-44-44000000-44-440000000000000000000000000004-400000000000000000000000000000000000
χ888-8-88800-80000000000000004-4-444i−4i−4i4i000000000000000000000000000004i−4i000000000000000000000000000000000
χ898-8-88800-80000000000000004-4-44−4i4i4i−4i00000000000000000000000000000−4i4i000000000000000000000000000000000
χ908-8-88800-8000000000000000-444-44i−4i−4i4i00000000000000000000000000000−4i4i000000000000000000000000000000000
χ918-8-88800-8000000000000000-444-4−4i4i4i−4i000000000000000000000000000004i−4i000000000000000000000000000000000
χ928-8-88-80080000000004-4-4400000000004-4-440000000000000000000000000004-40000000000000000000000000000000
χ938-8-88-80080000000004-4-440000000000-444-4000000000000000000000000000-440000000000000000000000000000000
χ948-8-88-8008000000000-444-400000000004-4-44000000000000000000000000000-440000000000000000000000000000000
χ958-8-88-8008000000000-444-40000000000-444-40000000000000000000000000004-40000000000000000000000000000000

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