Finite Group Databasebeta

← Group #11721762

Character table — Group #11721762

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82
size1111111111112222224444446666666666666666121212121212121212121212121212121212121212121212181818181818181818181818363636363636
order122233666666441212121244121212123333666666666666121212121212121212121212121212121212121212121212224466661212121224661212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111-1-1-1-1-1-11-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1-111
χ6111111111111-1-1-1-1-1-11-111-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-111-1-1
χ7111111111111-1-1-1-1-1-1-11-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-11-111-1-1
χ8111111111111-1-1-1-1-1-1-11-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-11-1-111
χ92222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000000000000000
χ10222222222222222222222222-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1000000000000000000
χ11222222222222222222222222-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122-1-1000000000000000000
χ12222222222222222222222222-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122-1-1-1-1-1-122-1-1-1-1-1-122000000000000000000
χ13222222222222222222-2-2-2-2-2-22-1-1-12-1-1-12-1-1-12-1-1-1-2-211111122-1-1-1-1-1-1-2-2111111000000000000000000
χ14222222222222222222-2-2-2-2-2-2-12-1-1-12-1-1-12-1-1-12-1-111-2-21111-1-122-1-1-1-111-2-21111000000000000000000
χ15222222222222222222-2-2-2-2-2-2-1-12-1-1-12-1-1-12-1-1-12-11111-2-211-1-1-1-122-1-11111-2-211000000000000000000
χ16222222222222222222-2-2-2-2-2-2-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2-1-1-1-1-1-122111111-2-2000000000000000000
χ17222222222222-2-2-2-2-2-22-222-2-22-1-1-12-1-1-12-1-1-12-1-1-122-1-1-1-1-1-1-2-2111111-2-2111111000000000000000000
χ18222222222222-2-2-2-2-2-22-222-2-2-12-1-1-12-1-1-12-1-1-12-1-1-1-122-1-1-1-111-2-2111111-2-21111000000000000000000
χ19222222222222-2-2-2-2-2-22-222-2-2-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-122-1-11111-2-2111111-2-211000000000000000000
χ20222222222222-2-2-2-2-2-22-222-2-2-1-1-12-1-1-12-1-1-12-1-1-12-1-1-1-1-1-122111111-2-2111111-2-2000000000000000000
χ21222222222222-2-2-2-2-2-2-22-2-2222-1-1-12-1-1-12-1-1-12-1-1-1-2-2111111-2-211111122-1-1-1-1-1-1000000000000000000
χ22222222222222-2-2-2-2-2-2-22-2-222-12-1-1-12-1-1-12-1-1-12-1-111-2-2111111-2-21111-1-122-1-1-1-1000000000000000000
χ23222222222222-2-2-2-2-2-2-22-2-222-1-12-1-1-12-1-1-12-1-1-12-11111-2-2111111-2-211-1-1-1-122-1-1000000000000000000
χ24222222222222-2-2-2-2-2-2-22-2-222-1-1-12-1-1-12-1-1-12-1-1-12111111-2-2111111-2-2-1-1-1-1-1-122000000000000000000
χ2522-2-22222-2-2-2-22i−2i2i2i−2i−2i0000002222-2-2-2-22222-2-2-2-2000000002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ2622-2-22222-2-2-2-22i−2i2i2i−2i−2i0000002-1-1-1-21112-1-1-1-211100−i3i3−i3i3−i3i32i−2i−ii−ii−ii003−33−33−3000000000000000000
χ2722-2-22222-2-2-2-22i−2i2i2i−2i−2i0000002-1-1-1-21112-1-1-1-211100i3−i3i3−i3i3−i32i−2i−ii−ii−ii00−33−33−33000000000000000000
χ2822-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-12-1-11-211-12-1-11-211−i3i300−i3i3i3−i3−ii2i−2i−ii−ii3−3003−3−33000000000000000000
χ2922-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-12-1-11-211-12-1-11-211i3−i300i3−i3−i3i3−ii2i−2i−ii−ii−3300−333−3000000000000000000
χ3022-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-1-12-111-21-1-12-111-21−i3i3i3−i300−i3i3−ii−ii2i−2i−ii3−3−33003−3000000000000000000
χ3122-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-1-12-111-21-1-12-111-21i3−i3−i3i300i3−i3−ii−ii2i−2i−ii−333−300−33000000000000000000
χ3222-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-1-1-12111-2-1-1-12111-2−i3i3−i3i3i3−i300−ii−ii−ii2i−2i3−33−3−3300000000000000000000
χ3322-2-22222-2-2-2-22i−2i2i2i−2i−2i000000-1-1-12111-2-1-1-12111-2i3−i3i3−i3−i3i300−ii−ii−ii2i−2i−33−333−300000000000000000000
χ3422-2-22222-2-2-2-2−2i2i−2i−2i2i2i0000002222-2-2-2-22222-2-2-2-200000000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ3522-2-22222-2-2-2-2−2i2i−2i−2i2i2i0000002-1-1-1-21112-1-1-1-211100−i3i3−i3i3−i3i3−2i2ii−ii−ii−i00−33−33−33000000000000000000
χ3622-2-22222-2-2-2-2−2i2i−2i−2i2i2i0000002-1-1-1-21112-1-1-1-211100i3−i3i3−i3i3−i3−2i2ii−ii−ii−i003−33−33−3000000000000000000
χ3722-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-12-1-11-211-12-1-11-211−i3i300−i3i3i3−i3i−i−2i2ii−ii−i−3300−333−3000000000000000000
χ3822-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-12-1-11-211-12-1-11-211i3−i300i3−i3−i3i3i−i−2i2ii−ii−i3−3003−3−33000000000000000000
χ3922-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-1-12-111-21-1-12-111-21−i3i3i3−i300−i3i3i−ii−i−2i2ii−i−333−300−33000000000000000000
χ4022-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-1-12-111-21-1-12-111-21i3−i3−i3i300i3−i3i−ii−i−2i2ii−i3−3−33003−3000000000000000000
χ4122-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-1-1-12111-2-1-1-12111-2−i3i3−i3i3i3−i300i−ii−ii−i−2i2i−33−333−300000000000000000000
χ4222-2-22222-2-2-2-2−2i2i−2i−2i2i2i000000-1-1-12111-2-1-1-12111-2i3−i3i3−i3−i3i300i−ii−ii−i−2i2i3−33−3−3300000000000000000000
χ432-22-222-2-222-2-200000000000022222222-2-2-2-2-2-2-2-2000000000000000000000000002i−2i00002i2i−2i−2i000000
χ442-22-222-2-222-2-200000000000022222222-2-2-2-2-2-2-2-200000000000000000000000000−2i2i0000−2i−2i2i2i000000
χ452-2-2222-2-2-2-2220000000000002222-2-2-2-2-2-2-2-222220000000000000000000000002-20022-2-20000000000
χ462-2-2222-2-2-2-2220000000000002222-2-2-2-2-2-2-2-22222000000000000000000000000-2200-2-2220000000000
χ473333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211−1−i32−1+i32−1−i32−1+i32
χ483333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i32-1-11+i321−i321+i321−i32
χ493333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i3200000000000000000000000000000000000000001111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11+i321−i321+i321−i32
χ503333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i3233−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i320000000000000000000000000000000000000000-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i3211−1−i32−1+i32−1−i32−1+i32
χ513333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32-111+i321−i32−1−i32−1+i32
χ523333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i323-3−3−3i32−3+3i323+3i323−3i320000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321-1−1−i32−1+i321+i321−i32
χ533333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i32000000000000000000000000000000000000000011-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321-1−1−i32−1+i321+i321−i32
χ543333−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32-3-33+3i323−3i323+3i323−3i32-333+3i323−3i32−3−3i32−3+3i320000000000000000000000000000000000000000-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32-111+i321−i32−1−i32−1+i32
χ553333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211−1+i32−1−i32−1+i32−1−i32
χ563333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i32-1-11−i321+i321−i321+i32
χ573333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i3200000000000000000000000000000000000000001111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11−i321+i321−i321+i32
χ583333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i3233−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i320000000000000000000000000000000000000000-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i3211−1+i32−1−i32−1+i32−1−i32
χ593333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32-111−i321+i32−1+i32−1−i32
χ603333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i323-3−3+3i32−3−3i323−3i323+3i320000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i321-1−1+i32−1−i321−i321+i32
χ613333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i32000000000000000000000000000000000000000011-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321-1−1+i32−1−i321−i321+i32
χ623333−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32−3+3i32−3−3i32-3-33−3i323+3i323−3i323+3i32-333−3i323+3i32−3+3i32−3−3i320000000000000000000000000000000000000000-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1−i32-111−i321+i32−1+i32−1−i32
χ634-44-444-4-444-4-40000000000004-2-2-24-2-2-2-4222-4222000000000000000000000000000000000000000000
χ644-44-444-4-444-4-4000000000000-24-2-2-24-2-22-4222-422000000000000000000000000000000000000000000
χ654-44-444-4-444-4-4000000000000-2-24-2-2-24-222-4222-42000000000000000000000000000000000000000000
χ664-44-444-4-444-4-4000000000000-2-2-24-2-2-24222-4222-4000000000000000000000000000000000000000000
χ674-4-4444-4-4-4-4440000000000004-2-2-2-4222-42224-2-2-2000000000000000000000000000000000000000000
χ684-4-4444-4-4-4-444000000000000-24-2-22-4222-422-24-2-2000000000000000000000000000000000000000000
χ694-4-4444-4-4-4-444000000000000-2-24-222-4222-42-2-24-2000000000000000000000000000000000000000000
χ704-4-4444-4-4-4-444000000000000-2-2-24222-4222-4-2-2-24000000000000000000000000000000000000000000
χ7166-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i36i−6i6ζ116ζ7−6ζ11−6ζ70000000000000000000000000000000000000000000000000000000000000000
χ7266-6-6−3−3i3−3+3i3−3−3i3−3+3i33+3i33−3i33+3i33−3i3−6i6i−6ζ11−6ζ76ζ116ζ70000000000000000000000000000000000000000000000000000000000000000
χ7366-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i36i−6i6ζ76ζ11−6ζ7−6ζ110000000000000000000000000000000000000000000000000000000000000000
χ7466-6-6−3+3i3−3−3i3−3+3i3−3−3i33−3i33+3i33−3i33+3i3−6i6i−6ζ7−6ζ116ζ76ζ110000000000000000000000000000000000000000000000000000000000000000
χ756-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i30000000000000000000000000000000000000000000000000000002i−2i00002ζ112ζ7−2ζ11−2ζ7000000
χ766-66-6−3−3i3−3+3i33+3i33−3i3−3−3i3−3+3i33+3i33−3i3000000000000000000000000000000000000000000000000000000−2i2i0000−2ζ11−2ζ72ζ112ζ7000000
χ776-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i30000000000000000000000000000000000000000000000000000002i−2i00002ζ72ζ11−2ζ7−2ζ11000000
χ786-66-6−3+3i3−3−3i33−3i33+3i3−3+3i3−3−3i33−3i33+3i3000000000000000000000000000000000000000000000000000000−2i2i0000−2ζ7−2ζ112ζ72ζ11000000
χ796-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i300000000000000000000000000000000000000000000000000002-200−1−i3−1+i31+i31−i30000000000
χ806-6-66−3−3i3−3+3i33+3i33−3i33+3i33−3i3−3−3i3−3+3i30000000000000000000000000000000000000000000000000000-22001+i31−i3−1−i3−1+i30000000000
χ816-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i300000000000000000000000000000000000000000000000000002-200−1+i3−1−i31−i31+i30000000000
χ826-6-66−3+3i3−3−3i33−3i33+3i33−3i33+3i3−3+3i3−3−3i30000000000000000000000000000000000000000000000000000-22001−i31+i3−1+i3−1−i30000000000

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