Finite Group Databasebeta

← Group #72231792

Character table — Group #72231792

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11222224444444448888888888881616161616161624242424323232323232323232323232323232324848484848484848484848484848
order12222362222226662244666666664444612122244444412121212121212121212121224444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111-1-1-1-11111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1
χ91111111-111-1-1-11111-11-1-1-111-1-1-1-1ii−i−i11-11-11-11-1i−iii−i−i11-1-1ii−i−i111-1-1-1ii−i−iii−i−i
χ101111111-111-1-1-11111-11-1-1-111-1-1-1-1ii−i−i11-11-11-1-11−iiii−i−i-1-111−i−iii-1-11-111ii−i−i−i−iii
χ111111111-111-1-1-11111-11-1-1-111-1-1-1-1ii−i−i11-1-11-111-1i−iii−i−i11-1-1ii−i−i-1-1-1111−i−iii−i−iii
χ121111111-111-1-1-11111-11-1-1-111-1-1-1-1ii−i−i11-1-11-11-11−iiii−i−i-1-111−i−iii11-11-1-1−i−iiiii−i−i
χ131111111-111-1-1-11111-11-1-1-111-1-1-1-1−i−iii11-11-11-11-1−ii−i−iii11-1-1−i−iii111-1-1-1−i−iii−i−iii
χ141111111-111-1-1-11111-11-1-1-111-1-1-1-1−i−iii11-11-11-1-11i−i−i−iii-1-111ii−i−i-1-11-111−i−iiiii−i−i
χ151111111-111-1-1-11111-11-1-1-111-1-1-1-1−i−iii11-1-11-111-1−ii−i−iii11-1-1−i−iii-1-1-1111ii−i−iii−i−i
χ161111111-111-1-1-11111-11-1-1-111-1-1-1-1−i−iii11-1-11-11-11i−i−i−iii-1-111ii−i−i11-11-1-1ii−i−i−i−iii
χ172222222222-2-22222-22-2-2222222-2-20000-2-2-22-22-2000000000000000000-220000000000
χ182222222222-2-22222-22-2-2222222-2-20000-2-2-2-22-220000000000000000002-20000000000
χ1922222222-2-22222222-2-2-222-2-2-2-2222-22-22-2-2000000002-22-20000000000000000000000
χ2022222222-2-22222222-2-2-222-2-2-2-222-22-222-2-200000000-22-220000000000000000000000
χ2122222222-2-2-2-22222-2-22222-2-2-2-2-2-20000-222000000000000000000000000002i−2i2i−2i0000
χ2222222222-2-2-2-22222-2-22222-2-2-2-2-2-20000-22200000000000000000000000000−2i2i−2i2i0000
χ232222222-22222-2222-2-2-22-2-222-2-2220000-2-222222000000000000000000-2-20000000000
χ242222222-22222-2222-2-2-22-2-222-2-2220000-2-22-2-2-2-2000000000000000000220000000000
χ252222222-2-2-222-2222-222-2-2-2-2-222220000-22-2000000000000000000000000002-2-220000
χ262222222-2-2-222-2222-222-2-2-2-2-222220000-22-200000000000000000000000000-222-20000
χ272222222-2-2-2-2-2-222222-22-2-2-2-222-2-22i−2i−2i2i2-22000000002i−2i−2i2i0000000000000000000000
χ282222222-2-2-2-2-2-222222-22-2-2-2-222-2-2−2i2i2i−2i2-2200000000−2i2i2i−2i0000000000000000000000
χ2922222-1-1222222-1-1-12222-1-1-1-1-1-1-1-12222-1-1-100002222-1-1-1-1-1-1-1-1-1-1-1-100000000000000
χ3022222-1-1222222-1-1-12222-1-1-1-1-1-1-1-12222-1-1-10000-2-2-2-2-1-1-1-11111111100000000000000
χ3122222-1-1222222-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1000022-2-21111-1-1-1-1111100000000000000
χ3222222-1-1222222-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-1-1-10000-2-22211111111-1-1-1-100000000000000
χ3322222-1-12-2-2222-1-1-12-2-2-2-1-11111-1-12-22-2-11100000000-11-113−33−33−33−300000000000000
χ3422222-1-12-2-2222-1-1-12-2-2-2-1-11111-1-12-22-2-11100000000-11-11−33−33−33−3300000000000000
χ3522222-1-12-2-2222-1-1-12-2-2-2-1-11111-1-1-22-22-111000000001-11-13−33−3−33−3300000000000000
χ3622222-1-12-2-2222-1-1-12-2-2-2-1-11111-1-1-22-22-111000000001-11-1−33−333−33−300000000000000
χ3722222-1-1-222-2-2-2-1-1-12-22-211-1-111112i2i−2i−2i-1-1100002-22i−2i−i−iii-1-111−i−iii00000000000000
χ3822222-1-1-222-2-2-2-1-1-12-22-211-1-111112i2i−2i−2i-1-110000-22−2i2i−i−iii11-1-1ii−i−i00000000000000
χ3922222-1-1-222-2-2-2-1-1-12-22-211-1-11111−2i−2i2i2i-1-1100002-2−2i2iii−i−i-1-111ii−i−i00000000000000
χ4022222-1-1-222-2-2-2-1-1-12-22-211-1-11111−2i−2i2i2i-1-110000-222i−2iii−i−i11-1-1−i−iii00000000000000
χ4122222-1-1-2-2-2-2-2-2-1-1-122-221111-1-1112i−2i−2i2i-11-100000000−iii−i3−3−33i3−i3−i3i300000000000000
χ4222222-1-1-2-2-2-2-2-2-1-1-122-221111-1-1112i−2i−2i2i-11-100000000−iii−i−333−3−i3i3i3−i300000000000000
χ4322222-1-1-2-2-2-2-2-2-1-1-122-221111-1-111−2i2i2i−2i-11-100000000i−i−ii3−3−33−i3i3i3−i300000000000000
χ4422222-1-1-2-2-2-2-2-2-1-1-122-221111-1-111−2i2i2i−2i-11-100000000i−i−ii−333−3i3−i3−i3i300000000000000
χ4544444-2-2444-4-44-2-2-2-44-4-4-2-2-2-2-2-22200002220000000000000000000000000000000000
χ4644444-2-24-4-4-4-44-2-2-2-4-444-2-222222200002-2-20000000000000000000000000000000000
χ4744444-2-2-44444-4-2-2-2-4-4-4422-2-222-2-2000022-20000000000000000000000000000000000
χ4844444-2-2-4-4-444-4-2-2-2-444-42222-2-2-2-200002-220000000000000000000000000000000000
χ4944-44-4440004-404-4-400000000004-40000000000000000000000000002-2002-200000000
χ5044-44-4440004-404-4-400000000004-4000000000000000000000000000-2200-2200000000
χ5144-44-444000-4404-4-40000000000-440000000000000000000000000002-200-2200000000
χ5244-44-444000-4404-4-40000000000-44000000000000000000000000000-22002-200000000
χ5344-4-444404-4000-44-40000004-400000000000040-4000000000000000000000000000000
χ5444-4-444404-4000-44-40000004-4000000000000-404000000000000000000000000000000
χ5544-4-44440-44000-44-4000000-440000000000040-40000000000000000000000000000000
χ5644-4-44440-44000-44-4000000-4400000000000-4040000000000000000000000000000000
χ57888-8-888000000-8-8800000000000000000000000000000000000000000000000000000
χ58888-8-8-4-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ59888-8-8-4-400000044-4000000004i3−4i30000000000000000000000000000000000000000000
χ6088-88-8-4-40008-80-4440000000000-4400000000000000000000000000000000000000000
χ6188-88-8-4-4000-880-44400000000004-400000000000000000000000000000000000000000
χ6288-8-88-4-408-80004-44000000-44000000000000000000000000000000000000000000000
χ6388-8-88-4-40-880004-440000004-4000000000000000000000000000000000000000000000
χ648-80008-840000-400000004-400000000000000000000000000000000000000000002i−2i2i−2i
χ658-80008-840000-400000004-40000000000000000000000000000000000000000000−2i2i−2i2i
χ668-80008-8-4000040000000-4400000000000000000000000000000000000000000002-2-22
χ678-80008-8-4000040000000-440000000000000000000000000000000000000000000-222-2
χ6816-16000-8880000-80000000-4400000000000000000000000000000000000000000000000
χ6916-16000-88-80000800000004-400000000000000000000000000000000000000000000000

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