Finite Group Databasebeta

← Group #11780756

Character table — Group #11780756

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222224444444448888888888888888816161616161624242424242424242424242424242424242448484872727272
order12223366666634446661212441212121212121212121212121212121212121212122444668812121212121224242424412128888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111-1-1111-1-111-1-1111111-1-1-1-1-1-111-1-11111-1-111-1-11111-1-1-111-1-1
χ6111111111111111111111-1-1111-1-111-1-1111111-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1111-1-111
χ7111111111111111111111-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-11111-1-1111111-1-1-1-1-111
χ8111111111111111111111-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-1-1-111111-1-1
χ922222222222222-2-2222222-2-2-2-2222-2-2-222-2-2-2-22-222-2-20000000000000000000000000
χ1022222222222222-2-222222-22-2-2-2-2-22-22222-2-2-2-2-22-2-2220000000000000000000000000
χ112222222222222-22-2222-2-20022-200-2-200-2-222-2-2000000002-20000-2-2002200000000000
χ122222222222222-22-2222-2-20022-200-2-200-2-222-2-200000000-2200002200-2-200000000000
χ132222222222222-2-22222-2-200-2-2200-2200-2-2-2-2220000002-200220000-2-20000000000000
χ142222222222222-2-22222-2-200-2-2200-2200-2-2-2-222000000-2200-2-20000220000000000000
χ1522222-122-1-12-1-1222-1-1-122222-12-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-100-1-1-1-1-1-100000000000
χ1622222-122-1-12-1-1222-1-1-122222-12-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2110011111100000000000
χ1722222-122-1-12-1-1222-1-1-122-2-22-1211-1-111-1-1-1-1-1-1-2-2111122-2-2-1-10011-1-11100000000000
χ1822222-122-1-12-1-1222-1-1-122-2-22-1211-1-111-1-1-1-1-1-1-2-21111-2-2221100-1-111-1-100000000000
χ1922222-122-1-12-1-12-2-2-1-1-1222-2-21-2-1-1-1111-1-111112-2-1-1110000−i3i300−i3i3−i3i3−i3i300000000000
χ2022222-122-1-12-1-12-2-2-1-1-1222-2-21-2-1-1-1111-1-111112-2-1-1110000i3−i300i3−i3i3−i3i3−i300000000000
χ2122222-122-1-12-1-12-2-2-1-1-122-22-21-211-11-1-1-1-11111-2211-1-10000−i3i300i3−i3−i3i3i3−i300000000000
χ2222222-122-1-12-1-12-2-2-1-1-122-22-21-211-11-1-1-1-11111-2211-1-10000i3−i300−i3i3i3−i3−i3i300000000000
χ2322222-122-1-12-1-1-22-2-1-1-1-2-2002-1-2−i3i311−i3i311-1-11100−i3i3−i3i3002-2−i3i30011i3−i3-1-100000000000
χ2422222-122-1-12-1-1-22-2-1-1-1-2-2002-1-2−i3i311−i3i311-1-11100−i3i3−i3i300-22i3−i300-1-1−i3i31100000000000
χ2522222-122-1-12-1-1-22-2-1-1-1-2-2002-1-2i3−i311i3−i311-1-11100i3−i3i3−i3002-2i3−i30011−i3i3-1-100000000000
χ2622222-122-1-12-1-1-22-2-1-1-1-2-2002-1-2i3−i311i3−i311-1-11100i3−i3i3−i300-22−i3i300-1-1i3−i31100000000000
χ2722222-122-1-12-1-1-2-22-1-1-1-2-200-212−i3i31-1i3−i31111-1-100−i3i3i3−i32-200-1-100i3−i311−i3i300000000000
χ2822222-122-1-12-1-1-2-22-1-1-1-2-200-212−i3i31-1i3−i31111-1-100−i3i3i3−i3-22001100−i3i3-1-1i3−i300000000000
χ2922222-122-1-12-1-1-2-22-1-1-1-2-200-212i3−i31-1−i3i31111-1-100i3−i3−i3i32-200-1-100−i3i311i3−i300000000000
χ3022222-122-1-12-1-1-2-22-1-1-1-2-200-212i3−i31-1−i3i31111-1-100i3−i3−i3i3-22001100i3−i3-1-1−i3i300000000000
χ312222-12-1-122-12-1222-1-1-1-1-122-12-1222222-1-1-1-1-1-1-1-1-1-1-1-100000022000000-1-1-1-12-1-10000
χ322222-12-1-122-12-1222-1-1-1-1-122-12-1222222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-20000001111-2110000
χ332222-12-1-122-12-1222-1-1-1-1-1-2-2-12-1-2-222-2-2-1-1-1-1-1-111111100000022000000-1-1-1-1-2110000
χ342222-12-1-122-12-1222-1-1-1-1-1-2-2-12-1-2-222-2-2-1-1-1-1-1-1111111000000-2-200000011112-1-10000
χ352222-12-1-122-12-12-2-2-1-1-1-1-12-21-21222-2-2-2-1-11111-11-1-11100000000000000−i3−i3i3i30−i3i30000
χ362222-12-1-122-12-12-2-2-1-1-1-1-12-21-21222-2-2-2-1-11111-11-1-11100000000000000i3i3−i3−i30i3−i30000
χ372222-12-1-122-12-12-2-2-1-1-1-1-1-221-21-2-22-222-1-111111-111-1-100000000000000−i3−i3i3i30i3−i30000
χ382222-12-1-122-12-12-2-2-1-1-1-1-1-221-21-2-22-222-1-111111-111-1-100000000000000i3i3−i3−i30−i3i30000
χ394444-24-2-244-24-2-44-4-2-2-22200-24200-4-40022-2-2220000000000000000000000000000000
χ404444-24-2-244-24-2-4-44-2-2-222002-4-200-44002222-2-20000000000000000000000000000000
χ414444-2-2-2-2-2-2-2-21444111-2-244-2-2-2-2-2-2-2-2-2111111-2-211110000000000000000000000000
χ424444-2-2-2-2-2-2-2-21444111-2-2-4-4-2-2-222-2-22211111122-1-1-1-10000000000000000000000000
χ434444-2-2-2-2-2-2-2-214-4-4111-2-24-4222-2-2-222211-1-1-1-1-2211-1-10000000000000000000000000
χ444444-2-2-2-2-2-2-2-214-4-4111-2-2-4422222-22-2-211-1-1-1-12-2-1-1110000000000000000000000000
χ454444-2-2-2-2-2-2-2-21-44-41112200-2-22−2i32i322−2i32i3-1-111-1-100i3−i3i3−i30000000000000000000000000
χ464444-2-2-2-2-2-2-2-21-44-41112200-2-222i3−2i3222i3−2i3-1-111-1-100−i3i3−i3i30000000000000000000000000
χ474444-2-2-2-2-2-2-2-21-4-44111220022-2−2i32i32-22i3−2i3-1-1-1-11100i3−i3−i3i30000000000000000000000000
χ484444-2-2-2-2-2-2-2-21-4-44111220022-22i3−2i32-2−2i32i3-1-1-1-11100−i3i3i3−i30000000000000000000000000
χ4944-4-4444-44-4-4-44000-44-400000000000000000000000000000000000000000000002-200
χ5044-4-4444-44-4-4-44000-44-40000000000000000000000000000000000000000000000-2200
χ514-44-444-44-4-4-444000-4-440000000000000000000000000000000000000000000000002i−2i
χ524-44-444-44-4-4-444000-4-44000000000000000000000000000000000000000000000000−2i2i
χ534-4-4444-4-4-444-440004-4-400000000000000000000000000000002i−2i0000002i−2i2i−2i0000000
χ544-4-4444-4-4-444-440004-4-40000000000000000000000000000000−2i2i000000−2i2i−2i2i0000000
χ554-4-44-2422-44-2-4-2000-222−2i32i300000000000−2i32i300000000000000002i−2i0000002ζ7−2ζ72ζ11−2ζ110000000
χ564-4-44-2422-44-2-4-2000-222−2i32i300000000000−2i32i30000000000000000−2i2i000000−2ζ72ζ7−2ζ112ζ110000000
χ574-4-44-2422-44-2-4-2000-2222i3−2i3000000000002i3−2i300000000000000002i−2i0000002ζ11−2ζ112ζ7−2ζ70000000
χ584-4-44-2422-44-2-4-2000-2222i3−2i3000000000002i3−2i30000000000000000−2i2i000000−2ζ112ζ11−2ζ72ζ70000000
χ5988-8-88-48-8-44-84-40004-4400000000000000000000000000000000000000000000000000
χ6088-8-8-48-448-84-8-40004-4400000000000000000000000000000000000000000000000000
χ6188-8-8-4-4-44-44442000-22-2000000000000000006i−6i0000000000000000000000000000000
χ6288-8-8-4-4-44-44442000-22-200000000000000000−6i6i0000000000000000000000000000000
χ638-88-88-4-8844-8-4-400044-400000000000000000000000000000000000000000000000000
χ648-88-8-484-4-8-848-400044-400000000000000000000000000000000000000000000000000
χ658-88-8-4-44-4444-42000-2-220000000000000006i−6i000000000000000000000000000000000
χ668-88-8-4-44-4444-42000-2-22000000000000000−6i6i000000000000000000000000000000000
χ678-8-888-4-8-84-484-4000-44400000000000000000000000000000000000000000000000000
χ688-8-88-4-4444-4-4420002-2-2−4i34i3000000000002i3−2i300000000000000000000000000000000000
χ698-8-88-4-4444-4-4420002-2-24i3−4i300000000000−2i32i300000000000000000000000000000000000

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