Finite Group Databasebeta

← Group #11780751

Character table — Group #11780751

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222222444444444448888888888161616161616161616242424242424242424242424242424244848484872727272
order122233666666344466612121212121212121212121212124121212121212121224448888242424242424242461212124488
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-11-111-1-11111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-11-11-1-111-1-1-1-11111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-11-1-1-111-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1111-1-11111-1-1-1-1-1-111-1-111
χ8111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ922222222222222-2-222222-2-22-2-2-222-2-2-2-2000000000020-200000000000000-220000
χ1022222222222222-2-222222-2-22-2-2-222-2-2-2-20000000000-202000000000000002-20000
χ112222222222222-22-2222-2-222-2-22-2-2-222-2-200000000020-200000000000002-2000000
χ122222222222222-22-2222-2-222-2-22-2-2-222-2-2000000000-2020000000000000-22000000
χ132222222222222-2-22222-2-2-2-2-22-22-2-2-2-222000000000000000000000000000002-200
χ142222222222222-2-22222-2-2-2-2-22-22-2-2-2-22200000000000000000000000000000-2200
χ1522222-12-1-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-120202200-1-1-1-10000-1-1000000
χ1622222-12-1-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1-1-1-20-20-2-2001111000011000000
χ1722222-12-1-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-1-211-2-211112020-2-20011110000-1-1000000
χ1822222-12-1-12-12-1222-1-1-122-1-1-1-122-1-1-1-1-1-1-211-2-21111-20-202200-1-1-1-1000011000000
χ1922222-12-1-12-12-1-22-2-1-1-1-2-2-1-1112-211-1-1110−i3i300−i3−i3i3i320-200000−i3−i3i3i30000-11000000
χ2022222-12-1-12-12-1-22-2-1-1-1-2-2-1-1112-211-1-1110−i3i300−i3−i3i3i3-20200000i3i3−i3−i300001-1000000
χ2122222-12-1-12-12-1-22-2-1-1-1-2-2-1-1112-211-1-1110i3−i300i3i3−i3−i320-200000i3i3−i3−i30000-11000000
χ2222222-12-1-12-12-1-22-2-1-1-1-2-2-1-1112-211-1-1110i3−i300i3i3−i3−i3-20200000−i3−i3i3i300001-1000000
χ232222-12-122-12-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-1020200220000-1-1-1-100-1-10000
χ242222-12-122-12-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-10-20-200-2-20000111100110000
χ252222-12-122-12-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2111111020200-2-20000111100-1-10000
χ262222-12-122-12-1-1222-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-21111110-20-200220000-1-1-1-100110000
χ272222-12-122-12-1-12-2-2-1-1-1-1-1-2-22-211-1-11111000−i3i3−i3i3−i3i3020-200000000−i3−i3i3i3001-10000
χ282222-12-122-12-1-12-2-2-1-1-1-1-1-2-22-211-1-11111000−i3i3−i3i3−i3i30-20200000000i3i3−i3−i300-110000
χ292222-12-122-12-1-12-2-2-1-1-1-1-1-2-22-211-1-11111000i3−i3i3−i3i3−i3020-200000000i3i3−i3−i3001-10000
χ302222-12-122-12-1-12-2-2-1-1-1-1-1-2-22-211-1-11111000i3−i3i3−i3i3−i30-20200000000−i3−i3i3i300-110000
χ3144444-24-2-24-24-24-4-4-2-2-24422-22-4-4-2-22222000000000000000000000000000000000
χ3244444-24-2-24-24-2-4-44-2-2-2-4-4222-2-442222-2-2000000000000000000000000000000000
χ334444-24-244-24-2-2-44-4-2-2-22244-4-4-2222-2-222000000000000000000000000000000000
χ344444-24-244-24-2-2-4-44-2-2-222-4-4-442-22222-2-2000000000000000000000000000000000
χ354444-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-2-21111114-2-2-2-21111000000000000000000000000
χ364444-2-2-2-2-2-2-2-21444111-2-2-2-2-2-2-2-2111111-42222-1-1-1-1000000000000000000000000
χ374444-2-2-2-2-2-2-2-214-4-4111-2-222-222211-1-1-1-1000−2i32i3i3−i3i3−i3000000000000000000000000
χ384444-2-2-2-2-2-2-2-214-4-4111-2-222-222211-1-1-1-10002i3−2i3−i3i3−i3i3000000000000000000000000
χ394444-2-2-2-2-2-2-2-21-44-411122-2-222-22-1-111-1-10−2i32i300i3i3−i3−i3000000000000000000000000
χ404444-2-2-2-2-2-2-2-21-44-411122-2-222-22-1-111-1-102i3−2i300−i3−i3i3i3000000000000000000000000
χ414444-2-2-2-2-2-2-2-21-4-4411122222-22-2-1-1-1-111000003-3-33000000000000000000000000
χ424444-2-2-2-2-2-2-2-21-4-4411122222-22-2-1-1-1-11100000-333-3000000000000000000000000
χ4344-4-444-4-44-4-444000-4-440000000000000000000000000000000000000000000002i−2i
χ4444-4-444-4-44-4-444000-4-44000000000000000000000000000000000000000000000−2i2i
χ454-44-44444-4-4-4-440004-4-4000000000000000000000000000002-200002-22-200000000
χ464-44-44444-4-4-4-440004-4-400000000000000000000000000000-220000-22-2200000000
χ474-44-4-24-24-42-42-2000-222−2i32i3000000−2i32i300000000000000000002-20000−1−i31+i3−1+i31−i300000000
χ484-44-4-24-24-42-42-2000-222−2i32i3000000−2i32i30000000000000000000-2200001+i3−1−i31−i3−1+i300000000
χ494-44-4-24-24-42-42-2000-2222i3−2i30000002i3−2i300000000000000000002-20000−1+i31−i3−1−i31+i300000000
χ504-44-4-24-24-42-42-2000-2222i3−2i30000002i3−2i30000000000000000000-2200001−i3−1+i31+i3−1−i300000000
χ514-4-4444-4-4-444-44000-44-40000000000000000000000000002i−2i002i−2i2i−2i000000000000
χ524-4-4444-4-4-444-44000-44-4000000000000000000000000000−2i2i00−2i2i−2i2i000000000000
χ534-4-444-2-4224-2-4-20002-2200−2i32i3000000−2i32i30000000000000002i−2i002ζ7−2ζ72ζ11−2ζ11000000000000
χ544-4-444-2-4224-2-4-20002-2200−2i32i3000000−2i32i3000000000000000−2i2i00−2ζ72ζ7−2ζ112ζ11000000000000
χ554-4-444-2-4224-2-4-20002-22002i3−2i30000002i3−2i30000000000000002i−2i002ζ11−2ζ112ζ7−2ζ7000000000000
χ564-4-444-2-4224-2-4-20002-22002i3−2i30000002i3−2i3000000000000000−2i2i00−2ζ112ζ11−2ζ72ζ7000000000000
χ5788-8-88-4-84-4-848-400044-400000000000000000000000000000000000000000000000
χ5888-8-8-484-884-8-4-400044-400000000000000000000000000000000000000000000000
χ5988-8-8-4-444-444-42000-2-220000000000006-6000000000000000000000000000000000
χ6088-8-8-4-444-444-42000-2-22000000000000-66000000000000000000000000000000000
χ618-88-88-48-44-84-8-4000-44400000000000000000000000000000000000000000000000
χ628-88-8-4-4-4-4444420002-2-2−4i34i30000002i3−2i30000000000000000000000000000000000000
χ638-88-8-4-4-4-4444420002-2-24i3−4i3000000−2i32i30000000000000000000000000000000000000
χ648-8-88-484-8-8-484-40004-4400000000000000000000000000000000000000000000000
χ658-8-88-4-4444-4-442000-22-200−4i34i30000002i3−2i300000000000000000000000000000000000
χ668-8-88-4-4444-4-442000-22-2004i3−4i3000000−2i32i300000000000000000000000000000000000

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