Finite Group Databasebeta

← Group #72324298

Character table — Group #72324298

Order 2048.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size112224444888881616161616161616161616161616161616161616161616161616161616161616323232323232646464646464646464646464128128128128
order12222222224444222222222222244444444444444444444444444444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i
χ411111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii
χ51111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11-11-1
χ61111111111111111111-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-11-11
χ71111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iiii−i−ii
χ81111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i−iii−i
χ9111111111111111-1-1-1-111-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ10111111111111111-1-1-1-111-1-11111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ11111111111111111-1-1-1-111-1-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111iiii−i−i−i−i−i−iii
χ12111111111111111-1-1-1-111-1-1-1-1-1-1111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111−i−i−i−iiiiiii−i−i
χ13111111111111111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1-11-11
χ14111111111111111-1-1-1-1-1-11111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1111-11-1
χ15111111111111111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1ii−i−i−i−iii−iii−i
χ16111111111111111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1−i−iiiii−i−ii−i−ii
χ1722222222222222-200002-2002222-22-200-2-2000022-2-200000000-2-22-200000000000000
χ1822222222222222-200002-200-2-2-2-2-22-200-2-2000022-2-20000000022-2200000000000000
χ1922222222222222-20000-22002222-2-2200-2-20000-2-22200000000-2-2-2200000000000000
χ2022222222222222-20000-2200-2-2-2-2-2-2200-2-20000-2-22200000000222-200000000000000
χ212222222222-2-2-2-2222-2-200002-22-220000-2-222-2-20000000022-2-22-20000000000000000
χ222222222222-2-2-2-2222-2-20000-22-2220000-2-222-2-200000000-2-222-220000000000000000
χ232222222222-2-2-2-22-2-22200002-22-220000-2-2-2-22200000000-2-2222-20000000000000000
χ242222222222-2-2-2-22-2-2220000-22-2220000-2-2-2-2220000000022-2-2-220000000000000000
χ252222222222-2-2-2-2-20000002-22-22-2-2002-2220000000022-2-20000-22002-2000000000000
χ262222222222-2-2-2-2-20000002-2-22-22-2002-2220000000022-2-200002-200-22000000000000
χ272222222222-2-2-2-2-2000000-222-22-2-200-222200000000-2-2220000-2200-22000000000000
χ282222222222-2-2-2-2-2000000-22-22-22-200-222200000000-2-22200002-2002-2000000000000
χ294444444-4-4-400004004400000000-400000000-4-4000000000000000000000000000000
χ304444444-4-4-40000400-4-400000000-40000000044000000000000000000000000000000
χ314444444-4-4-40000-44400000000004000000-4-400000000000000000000000000000000
χ324444444-4-4-40000-4-4-4000000000040000004400000000000000000000000000000000
χ3344444-4-444-444-4-400000040000000040000000000-4-400000000000000000000000000
χ3444444-4-444-444-4-4000000-400000000-400000000004400000000000000000000000000
χ3544444-4-444-4-4-444000004000000004000000000-4-40000000000000000000000000000
χ3644444-4-444-4-4-44400000-400000000-4000000000440000000000000000000000000000
χ3744444-4-4-4-4400000000000040000000044-40000000000-4-40000000000000000000000
χ3844444-4-4-4-44000000000000-400000000-44-40000000000440000000000000000000000
χ3944444-4-4-4-440000000000040000000040-4400000000-4-4000000000000000000000000
χ4044444-4-4-4-4400000000000-400000000-40-440000000044000000000000000000000000
χ4144-4-44004-40004-402-22-200220000000-2-2002-22-24-4002-22-20000000000000000000000
χ4244-4-44004-40004-402-22-200-2-2000000022002-22-2-4400-22-220000000000000000000000
χ4344-4-44004-40004-40-22-2200220000000-2-200-22-22-44002-22-20000000000000000000000
χ4444-4-44004-40004-40-22-2200-2-200000002200-22-224-400-22-220000000000000000000000
χ4544-4-44004-4000-4402-2-22402-200000-40-22002-2-2200002-2-220000000000000000000000
χ4644-4-44004-4000-4402-2-22-40-2200000402-2002-2-220000-222-20000000000000000000000
χ4744-4-44004-4000-440-222-240-2200000-402-200-222-20000-222-20000000000000000000000
χ4844-4-44004-4000-440-222-2-402-20000040-2200-222-200002-2-220000000000000000000000
χ4944-4-4400-4404-40002-22-2042-2000000-4-2200-22-220000-222-20000000000000000000000
χ5044-4-4400-4404-40002-22-20-4-2200000042-200-22-2200002-2-220000000000000000000000
χ5144-4-4400-4404-4000-22-2204-22000000-42-2002-22-200002-2-220000000000000000000000
χ5244-4-4400-4404-4000-22-220-42-20000004-22002-22-20000-222-20000000000000000000000
χ5344-4-4400-440-440002-2-2200220000000-2-200-222-2004-4-22-220000000000000000000000
χ5444-4-4400-440-440002-2-2200-2-200000002200-222-200-442-22-20000000000000000000000
χ5544-4-4400-440-44000-222-200220000000-2-2002-2-2200-44-22-220000000000000000000000
χ5644-4-4400-440-44000-222-200-2-2000000022002-2-22004-42-22-20000000000000000000000
χ57888-8-8000000000000000000040-400000000000000000000000000000002i−2i002i−2i0000
χ58888-8-8000000000000000000040-40000000000000000000000000000000−2i2i00−2i2i0000
χ59888-8-80000000000000000000-40400000000000000000000000000000002-200-220000
χ60888-8-80000000000000000000-4040000000000000000000000000000000-22002-20000
χ6188-88-800000000000000000040-40000000000000000000000000000002i−2i002i−2i000000
χ6288-88-800000000000000000040-4000000000000000000000000000000−2i2i00−2i2i000000
χ6388-88-8000000000000000000-4040000000000000000000000000000002-200-22000000
χ6488-88-8000000000000000000-404000000000000000000000000000000-22002-2000000
χ6516-160008-8000000000000000000000000000000000000000004-4000000000000000000
χ6616-160008-800000000000000000000000000000000000000000-44000000000000000000
χ6716-16000-880000000000000000000000000000000000000004-400000000000000000000
χ6816-16000-88000000000000000000000000000000000000000-4400000000000000000000

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