Finite Group Databasebeta

← Group #11780645

Character table — Group #11780645

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size111122222222444444444444488888888888161616161616161624242424242424242424242424242424242448484872727272
order122233666666344466612121212121224121212121212121212666612121212888888242424242424242424242424412122444
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-11-11-1
χ61111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111-11-11
χ71111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-11
χ81111111111111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-11-1
χ922222222222222-2-222222-2-2-2-2002-2-222-2-2-2-200000000000000000000000000000020-2
χ1022222222222222-2-222222-2-2-2-2002-2-222-2-2-2-2000000000000000000000000000000-202
χ112222222222222-22-2222-2-2-2-2222-2-2-22-2-2-2-2222222-2-2-2-20000000000000000000000000
χ122222222222222-22-2222-2-2-2-222-22-2-22-2-2-2-222-2-2-2-222220000000000000000000000000
χ132222222222222-2-22222-2-222-2-200-22-2-2-222-2-20000000000000000000000000000020-20
χ142222222222222-2-22222-2-222-2-200-22-2-2-222-2-200000000000000000000000000000-2020
χ1522222-122-1-12-1-1222-1-1-12222-1-122-1-12-1-1-1-1-1-12-1-1-12-1-1-100002200000000-1-1-1-12-1-10000
χ1622222-122-1-12-1-1222-1-1-12222-1-122-1-12-1-1-1-1-1-12-1-1-12-1-1-10000-2-2000000001111-2110000
χ1722222-122-1-12-1-1222-1-1-12222-1-1-2-2-1-12-1-1-1-1-1-1-2111-211100002200000000-1-1-1-1-2110000
χ1822222-122-1-12-1-1222-1-1-12222-1-1-2-2-1-12-1-1-1-1-1-1-2111-21110000-2-20000000011112-1-10000
χ1922222-122-1-12-1-1-22-2-1-1-1-2-2-2-2-1-12-21121111-1-12-1-1-1-211100000000000000−i3−i3i3i30−i3i30000
χ2022222-122-1-12-1-1-22-2-1-1-1-2-2-2-2-1-12-21121111-1-12-1-1-1-211100000000000000i3i3−i3−i30i3−i30000
χ2122222-122-1-12-1-1-22-2-1-1-1-2-2-2-2-1-1-221121111-1-1-21112-1-1-100000000000000−i3−i3i3i30i3−i30000
χ2222222-122-1-12-1-1-22-2-1-1-1-2-2-2-2-1-1-221121111-1-1-21112-1-1-100000000000000i3i3−i3−i30−i3i30000
χ232222-12-1-122-12-1222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-1-1-12-1-1222200-1-1-1-1-1-1-1-100000000000
χ242222-12-1-122-12-1222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-1-1-12-1-1-2-2-2-2001111111100000000000
χ252222-12-1-122-12-1222-1-1-1-1-1-1-122-2-222-1-1-1-1-1-1-11-2111-21122-2-200-1-1-1-1111100000000000
χ262222-12-1-122-12-1222-1-1-1-1-1-1-122-2-222-1-1-1-1-1-1-11-2111-211-2-222001111-1-1-1-100000000000
χ272222-12-1-122-12-1-22-2-1-1-11111222-2-2-2-11111-1-1-12-1-11-21100000033−3−333−3−300000000000
χ282222-12-1-122-12-1-22-2-1-1-11111222-2-2-2-11111-1-1-12-1-11-211000000−3−333−3−33300000000000
χ292222-12-1-122-12-1-22-2-1-1-1111122-22-2-2-11111-1-11-211-12-1-100000033−3−3−3−33300000000000
χ302222-12-1-122-12-1-22-2-1-1-1111122-22-2-2-11111-1-11-211-12-1-1000000−3−33333−3−300000000000
χ3144444-244-2-24-2-24-4-4-2-2-244-4-42200-22-4-2-22222000000000000000000000000000000000
χ3244444-244-2-24-2-2-4-44-2-2-2-4-44422002-2-422-2-222000000000000000000000000000000000
χ334444-24-2-244-24-24-4-4-2-2-2-2-222-4-4004-42-2-22222000000000000000000000000000000000
χ344444-24-2-244-24-2-4-44-2-2-222-2-2-4-400-44222-2-222000000000000000000000000000000000
χ354444-2-2-2-2-2-2-2-21444111-2-2-2-2-2-244-2-2-2111111-2-211-2-2110000000000000000000000000
χ364444-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-4-4-2-2-211111122-1-122-1-10000000000000000000000000
χ374444-2-2-2-2-2-2-2-214-4-4111-2-2222200-22211-1-1-1-1003-3003-30000000000000000000000000
χ384444-2-2-2-2-2-2-2-214-4-4111-2-2222200-22211-1-1-1-100-3300-330000000000000000000000000
χ394444-2-2-2-2-2-2-2-21-44-41112222-2-24-422-2-1-1-1-111-2-21122-1-10000000000000000000000000
χ404444-2-2-2-2-2-2-2-21-44-41112222-2-2-4422-2-1-1-1-11122-1-1-2-2110000000000000000000000000
χ414444-2-2-2-2-2-2-2-21-4-4411122-2-222002-22-1-111-1-1003-300-330000000000000000000000000
χ424444-2-2-2-2-2-2-2-21-4-4411122-2-222002-22-1-111-1-100-33003-30000000000000000000000000
χ4344-4-4444-44-4-4-440004-4-400000000000000000000000002-200002-22-2000000000000000
χ4444-4-4444-44-4-4-440004-4-40000000000000000000000000-220000-22-22000000000000000
χ4544-4-4-24-224-42-4-2000-2220023−2300000000023−2300000000002-20000−1+31−3−1−31+3000000000000000
χ4644-4-4-24-224-42-4-2000-2220023−2300000000023−230000000000-2200001−3−1+31+3−1−3000000000000000
χ4744-4-4-24-224-42-4-2000-22200−2323000000000−232300000000002-20000−1−31+3−1+31−3000000000000000
χ4844-4-4-24-224-42-4-2000-22200−2323000000000−23230000000000-2200001+3−1−31−3−1+3000000000000000
χ494-44-444-4-4-4-4444000-4-44000000000000000000000000000002-2000000002-22-20000000
χ504-44-444-4-4-4-4444000-4-4400000000000000000000000000000-2200000000-22-220000000
χ514-44-44-2-4-4224-2-200022-20000−2i32i3000000000−2i32i30000000000002-200000000−1−i31+i3−1+i31−i30000000
χ524-44-44-2-4-4224-2-200022-20000−2i32i3000000000−2i32i3000000000000-22000000001+i3−1−i31−i3−1+i30000000
χ534-44-44-2-4-4224-2-200022-200002i3−2i30000000002i3−2i30000000000002-200000000−1+i31−i3−1−i31+i30000000
χ544-44-44-2-4-4224-2-200022-200002i3−2i30000000002i3−2i3000000000000-22000000001−i3−1+i31+i3−1−i30000000
χ554-4-4444-44-44-4-44000-44-40000000000000000000000000002i−2i0000002i−2i2i−2i00000000000
χ564-4-4444-44-44-4-44000-44-4000000000000000000000000000−2i2i000000−2i2i−2i2i00000000000
χ574-4-44-242-2-442-4-20002-2223−2300000000023−23000000000000002i−2i000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000
χ584-4-44-242-2-442-4-20002-2223−2300000000023−2300000000000000−2i2i000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000
χ594-4-44-242-2-442-4-20002-22−2323000000000−2323000000000000002i−2i000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000
χ604-4-44-242-2-442-4-20002-22−2323000000000−232300000000000000−2i2i000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000
χ6188-8-88-48-8-44-84-4000-44400000000000000000000000000000000000000000000000000
χ6288-8-8-4-4-44-444420002-2-20043−43000000000−232300000000000000000000000000000000000
χ6388-8-8-4-4-44-444420002-2-200−434300000000023−2300000000000000000000000000000000000
χ648-88-8-4844-8-8-48-400044-400000000000000000000000000000000000000000000000000
χ658-88-8-4-44444-4-42000-2-220000−4i34i30000000002i3−2i3000000000000000000000000000000000
χ668-88-8-4-44444-4-42000-2-2200004i3−4i3000000000−2i32i3000000000000000000000000000000000
χ678-8-888-4-884-4-84-40004-4400000000000000000000000000000000000000000000000000
χ688-8-88-4-44-44-4442000-22-243−43000000000−23230000000000000000000000000000000000000
χ698-8-88-4-44-44-4442000-22-2−434300000000023−230000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.