Finite Group Databasebeta

← Group #72324255

Character table — Group #72324255

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222222448888888888888888888888888161616161616161616161616161616161616161616161616161632323232323232323232323232323232646464646464128128128128
order12222222222222222222222222222444444442224444444444444444444444424444444444444444444444888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-111-1-1111-1-11-1-111-1-1-1-111-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111-1-11-1-1-1-11111-1-111
χ511111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-1111-1-1111111-1-1-1-1
χ611111111111111111111111-1-1-1-11111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111-1-11-1-1-1-111111-1-1-1-1-1-111
χ811111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-111-1-1-1-11-1-1-1-1111-1-1111111-1-1
χ9111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-111-1-1111111-1111-1-1111-1-11-1-1-111-1-11-11-1
χ10111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1111-1-111-1-1-1-1-1-111-1-111-1-1111-1-11-1-1-11-1-1111-1-11-111-1-111-11-11
χ11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-111-1-11111111-1111-11-111-11-1-11-1-1-1-1111-1-11
χ12111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-11111-1-1-1-1-1-1-1-111-1-111111-1-1-11-1-1-11-111-11-1-111111-1-1-111-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1111111-1-11111-1-111111-11111-1-1-1-11-1-1-11-1-111-1-1-11-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-111-1-1111111-1-11111-1-1111-1-1-11-1-11-1-1-1-11-1-1-1111-1-1111-11-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111111111-111-11-1-1-1-11-11-1-1-1-1-111-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-1-1-111111111-1-1-1-111111-1-11-1-1-1-11-1-1-1-11-11-11111-1-11-1-11
χ17222222222222222222222220000222222222200-200000000000000002222-2-2-2000000-2-2-200-2-2-2000000000000
χ1822222222222222222222222000022-2-2-2-2-2-2-2-200-20000000000000000-2-2-2-2-2-2-200000022-20022-2000000000000
χ19222222222222222-2-2-2-2-2-2-2-20000222222-2-2-2-200-2000000000000000022-2-2-2-2-2000000-22200-222000000000000
χ20222222222222222-2-2-2-2-2-2-2-2000022-2-2-2-2222200-20000000000000000-2-222-2-2-20000002-22002-22000000000000
χ212222222222222-2-22222-2-2-2-20000-2-20000000000-222220000000022220000-22200-2-20000-200002-2-20000000000
χ222222222222222-2-22222-2-2-2-20000-2-20000000000-2-2-2-2-200000000-2-2-2-20000-22200220000-200002220000000000
χ232222222222222-2-22222-2-2-2-22222-2-20000000022200002222-2-2-2-2000000002-2-2000000002-2-200-2000000000000
χ242222222222222-2-22222-2-2-2-2-2-2-2-2-2-200000000-2-220000-2-2-2-22222000000002-2-20000000022200-2000000000000
χ252222222222222-2-2-2-2-2-222220000-2-20000000000-222-2-20000000022-2-20000-22200-22000020000-2-220000000000
χ262222222222222-2-2-2-2-2-222220000-2-20000000000-2-2-22200000000-2-2220000-222002-2000020000-22-20000000000
χ272222222222222-2-2-2-2-2-222222222-2-200000000-2-22000022-2-22222000000002-2-200000000-2-2-2002000000000000
χ282222222222222-2-2-2-2-2-22222-2-2-2-2-2-2000000002220000-2-222-2-2-2-2000000002-2-200000000-222002000000000000
χ292222222222-2-2-22-20000000000002-20000222222-2220000-2-222-2-2-2-20000-2-222-200-2000020000-20200000000000
χ302222222222-2-2-22-20000000000002-200002222-2-2-2-2-2000022-2-222220000-2-222-2002000020000-20-200000000000
χ312222222222-2-2-22-20000000000002-20000-2-2-2-222-2-2-20000-2-222-2-22200002222-20020000-2000020-200000000000
χ322222222222-2-2-22-20000000000002-20000-2-2-2-2-2-2-222000022-2-222-2-200002222-200-20000-2000020200000000000
χ332222222222-2-2-22-20000000022222-20000222200200-2-2-2-2000000002200-2-2-2-22000-2000-202-2020020000000000
χ342222222222-2-2-22-20000000022222-20000-2-2-2-20020022-2-200000000-2-20022-2-220002000202-20-200-20000000000
χ352222222222-2-2-22-200000000-2-2-2-22-20000222200200222200000000-2-200-2-2-2-220002000-20-220200-20000000000
χ362222222222-2-2-22-200000000-2-2-2-22-20000-2-2-2-200200-2-22200000000220022-2-22000-200020-220-20020000000000
χ372222222222-2-2-2-22000000000000-222222000022-2002200-2-2-2-22200-2-2-2-2002-22000-20020000-200020000000000
χ382222222222-2-2-2-22000000000000-2222220000-2-2-200-2-2002222-2-20022-2-2002-2200020020000-2000-20000000000
χ392222222222-2-2-2-22000000000000-22-2-2-2-2000022-200-2-200-2-2-2-222002222002-22000200-200002000-20000000000
χ402222222222-2-2-2-22000000000000-22-2-2-2-20000-2-2-20022002222-2-200-2-222002-22000-200-20000200020000000000
χ412222222222-2-2-2-22000000002222-2222220000002-2-200-2-20000002200-2-200-22-200-2000-200-22200200000000000
χ422222222222-2-2-2-22000000002222-22-2-2-2-200000022200-2-2000000-2-2002200-22-2002000200-22-200-200000000000
χ432222222222-2-2-2-2200000000-2-2-2-2-2222220000002220022000000-2-200-2-200-22-2002000-2002-2200-200000000000
χ442222222222-2-2-2-2200000000-2-2-2-2-22-2-2-2-20000002-2-2002200000022002200-22-200-20002002-2-200200000000000
χ4544444-4-44-4-4000040000000000000-44i4i−4i−4i0000000000000000000000000000002-2002-20000000000002i−2i000000
χ4644444-4-44-4-4000040000000000000-44i4i−4i−4i000000000000000000000000000000-2200-22000000000000−2i2i000000
χ4744444-4-44-4-4000040000000000000-4−4i−4i4i4i0000000000000000000000000000002-2002-2000000000000−2i2i000000
χ4844444-4-44-4-4000040000000000000-4−4i−4i4i4i000000000000000000000000000000-2200-220000000000002i−2i000000
χ494444-44-4-44-400040000000000000-4000004i4i−4i−4i000000000000000000000000002-200-22000000000000002i−2i0000
χ504444-44-4-44-400040000000000000-4000004i4i−4i−4i00000000000000000000000000-22002-200000000000000−2i2i0000
χ514444-44-4-44-400040000000000000-400000−4i−4i4i4i000000000000000000000000002-200-2200000000000000−2i2i0000
χ524444-44-4-44-400040000000000000-400000−4i−4i4i4i00000000000000000000000000-22002-2000000000000002i−2i0000
χ534444-4-44-4-4444-40044-4-4000000000000000000000000000000000000000000002200-2-200000000002-200000000
χ544444-4-44-4-4444-40044-4-400000000000000000000000000000000000000000000-2-200220000000000-2200000000
χ554444-4-44-4-4444-400-4-444000000000000000000000000000000000000000000002200-2-20000000000-2200000000
χ564444-4-44-4-4444-400-4-44400000000000000000000000000000000000000000000-2-2002200000000002-200000000
χ5744-4-400400-44-4000004-4000022-2-2002i−2i2i−2i2i−2i2i−2i2-202i−2i2i−2i2-22-200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000
χ5844-4-400400-44-4000004-4000022-2-200−2i2i−2i2i−2i2i−2i2i2-20−2i2i−2i2i2-22-20000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000
χ5944-4-400400-44-4000004-40000-2-222002i−2i2i−2i2i−2i2i−2i-220−2i2i−2i2i-22-220000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000
χ6044-4-400400-44-4000004-40000-2-22200−2i2i−2i2i−2i2i−2i2i-2202i−2i2i−2i-22-2200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000
χ6144-4-400400-44-400000-44000022-2-2002i−2i2i−2i−2i2i−2i2i-2202i−2i−2i2i2-2-2200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000
χ6244-4-400400-44-400000-44000022-2-200−2i2i−2i2i2i−2i2i−2i-220−2i2i2i−2i2-2-220000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000
χ6344-4-400400-44-400000-440000-2-222002i−2i2i−2i−2i2i−2i2i2-20−2i2i2i−2i-222-20000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000
χ6444-4-400400-44-400000-440000-2-22200−2i2i−2i2i2i−2i2i−2i2-202i−2i−2i2i-222-200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000
χ6544-4-400400-4-440004-400000022-2-2002i−2i2i−2i2i−2i2i−2i-220−2i2i−2i2i-222-200002i−2i2i−2i−2i2i−2i2i00000000000000000000000000000
χ6644-4-400400-4-440004-400000022-2-200−2i2i−2i2i−2i2i−2i2i-2202i−2i2i−2i-222-20000−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000
χ6744-4-400400-4-440004-4000000-2-222002i−2i2i−2i2i−2i2i−2i2-202i−2i2i−2i2-2-220000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000
χ6844-4-400400-4-440004-4000000-2-22200−2i2i−2i2i−2i2i−2i2i2-20−2i2i−2i2i2-2-2200002i−2i2i−2i2i−2i2i−2i00000000000000000000000000000
χ6944-4-400400-4-44000-4400000022-2-2002i−2i2i−2i−2i2i−2i2i2-20−2i2i2i−2i-22-2200002i−2i−2i2i−2i2i2i−2i00000000000000000000000000000
χ7044-4-400400-4-44000-4400000022-2-200−2i2i−2i2i2i−2i2i−2i2-202i−2i−2i2i-22-220000−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000
χ7144-4-400400-4-44000-44000000-2-222002i−2i2i−2i−2i2i−2i2i-2202i−2i−2i2i2-22-20000−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000
χ7244-4-400400-4-44000-44000000-2-22200−2i2i−2i2i2i−2i2i−2i-220−2i2i2i−2i2-22-200002i−2i−2i2i2i−2i−2i2i00000000000000000000000000000
χ7388888-8-88-8-80000-800000000000008000000000000000000000000000000000000000000000000000000000000
χ748888-88-8-88-8000-8000000000000080000000000000000000000000000000000000000000000000000000000000
χ758888-8-88-8-88-8-880000000000000000000000000000000000000000000000000000000000000000000000000000
χ7688-8-800-800800000000044-4-40000004-4-444-4-440000000000000000000000000000000000000000000000000000
χ7788-8-800-800800000000044-4-4000000-444-4-444-40000000000000000000000000000000000000000000000000000
χ7888-8-800-8008000000000-4-4440000004-4-44-444-40000000000000000000000000000000000000000000000000000
χ7988-8-800-8008000000000-4-444000000-444-44-4-440000000000000000000000000000000000000000000000000000
χ808-88-80-800800000000004-44-44-44-4000000000000000000000004-40000000000000000000000000000000000000
χ818-88-80-800800000000004-44-4-44-4400000000000000000000000-440000000000000000000000000000000000000
χ828-88-80-80080000000000-44-444-44-400000000000000000000000-440000000000000000000000000000000000000
χ838-88-80-80080000000000-44-44-44-44000000000000000000000004-40000000000000000000000000000000000000
χ848-8-88-8008000000000004-4-444-4-440000000000000000000004-4000000000000000000000000000000000000000
χ858-8-88-8008000000000004-4-44-444-4000000000000000000000-44000000000000000000000000000000000000000
χ868-8-88-800800000000000-444-44-4-44000000000000000000000-44000000000000000000000000000000000000000
χ878-8-88-800800000000000-444-4-444-40000000000000000000004-4000000000000000000000000000000000000000
χ8816-1616-1601600-1600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ8916-16-16161600-16000000000000000000000000000000000000000000000000000000000000000000000000000000000

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