Finite Group Databasebeta

← Group #11780647

Character table — Group #11780647

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222224444444444488888888888888881616161616162424242424242424242424242424242424242424242424247272144
order122233666666344466612121212441212121212121212121212121212121212121212224466668888121212122424242424242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111
χ511111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1
χ611111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-11111-1-11
χ711111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-11
χ811111111111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111111-1
χ922222222222222-2-222222-2-200-2-22-20000-2-222-2-200000020-2022000000-2-20000000000000
χ1022222222222222-2-222222-2-200-2-22-20000-2-222-2-2000000-2020-2-2000000220000000000000
χ112222222222222-22-2222-2-22200-2-2-220000-2-2-2-222000000020-20022000000-2-200000000000
χ122222222222222-22-2222-2-22200-2-2-220000-2-2-2-2220000000-20200-2-20000002200000000000
χ132222222222222-2-22222-2-2-2-22-222-2-222-2-222-2-2-2-22-222-2-2000000000000000000000000000
χ142222222222222-2-22222-2-2-2-2-2222-2-2-2-22222-2-2-2-2-22-2-222000000000000000000000000000
χ1522222-12-122-1-1-1222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-10000-1-1-1-100000000000
χ1622222-12-122-1-1-1222-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-211110000111100000000000
χ1722222-12-122-1-1-1222-1-1-12222-2-22-1-1-11111-1-1-1-1-1-1-2-211112-22-2-1-1110000-1-11100000000000
χ1822222-12-122-1-1-1222-1-1-12222-2-22-1-1-11111-1-1-1-1-1-1-2-21111-22-2211-1-1000011-1-100000000000
χ1922222-12-122-1-1-12-2-2-1-1-122-2-200-21-11−i3i3−i3i311-1-11100−i3i3−i3i320-20-1-1−i3i3000011−i3i300000000000
χ2022222-12-122-1-1-12-2-2-1-1-122-2-200-21-11−i3i3−i3i311-1-11100−i3i3−i3i3-202011i3−i30000-1-1i3−i300000000000
χ2122222-12-122-1-1-12-2-2-1-1-122-2-200-21-11i3−i3i3−i311-1-11100i3−i3i3−i320-20-1-1i3−i3000011i3−i300000000000
χ2222222-12-122-1-1-12-2-2-1-1-122-2-200-21-11i3−i3i3−i311-1-11100i3−i3i3−i3-202011−i3i30000-1-1−i3i300000000000
χ2322222-12-122-1-1-1-22-2-1-1-1-2-22200-211-1−i3i3i3−i31111-1-100−i3i3i3−i3020-2−i3i3-1-10000−i3i31100000000000
χ2422222-12-122-1-1-1-22-2-1-1-1-2-22200-211-1−i3i3i3−i31111-1-100−i3i3i3−i30-202i3−i3110000i3−i3-1-100000000000
χ2522222-12-122-1-1-1-22-2-1-1-1-2-22200-211-1i3−i3−i3i31111-1-100i3−i3−i3i3020-2i3−i3-1-10000i3−i31100000000000
χ2622222-12-122-1-1-1-22-2-1-1-1-2-22200-211-1i3−i3−i3i31111-1-100i3−i3−i3i30-202−i3i3110000−i3i3-1-100000000000
χ2722222-12-122-1-1-1-2-22-1-1-1-2-2-2-22-22-111-1-111-1-111112-2-1-1110000−i3i3−i3i30000i3−i3i3−i300000000000
χ2822222-12-122-1-1-1-2-22-1-1-1-2-2-2-22-22-111-1-111-1-111112-2-1-1110000i3−i3i3−i30000−i3i3−i3i300000000000
χ2922222-12-122-1-1-1-2-22-1-1-1-2-2-2-2-222-11111-1-1-1-11111-2211-1-10000−i3i3i3−i30000i3−i3−i3i300000000000
χ3022222-12-122-1-1-1-2-22-1-1-1-2-2-2-2-222-11111-1-1-1-11111-2211-1-10000i3−i3−i3i30000−i3i3i3−i300000000000
χ312222-12-12-1-122-1222-1-1-1-1-1-1-122-12222222-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-1000
χ322222-12-12-1-122-1222-1-1-1-1-1-1-122-12222222-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-2000011111111000
χ332222-12-12-1-122-1222-1-1-1-1-1-1-1-2-2-1222-2-2-2-2-1-1-1-1-1-11111110000000022-2-20000-1-1-1-11111000
χ342222-12-12-1-122-1222-1-1-1-1-1-1-1-2-2-1222-2-2-2-2-1-1-1-1-1-111111100000000-2-22200001111-1-1-1-1000
χ352222-12-12-1-122-1-2-22-1-1-111112-2-12-2-222-2-2-1-11111-11-1-111000000000000000033−3−333−3−3000
χ362222-12-12-1-122-1-2-22-1-1-111112-2-12-2-222-2-2-1-11111-11-1-1110000000000000000−3−333−3−333000
χ372222-12-12-1-122-1-2-22-1-1-11111-22-12-2-2-2-222-1-111111-111-1-1000000000000000033−3−3−3−333000
χ382222-12-12-1-122-1-2-22-1-1-11111-22-12-2-2-2-222-1-111111-111-1-10000000000000000−3−33333−3−3000
χ394444-24-24-2-244-24-4-4-2-2-2-2-222002-44-4000022-2-222000000000000000000000000000000000
χ404444-24-24-2-244-2-44-4-2-2-222-2-2002-4-4400002222-2-2000000000000000000000000000000000
χ414444-2-2-2-2-2-2-2-21444111-2-2-2-244-2-2-2-2-2-2-2-2111111-2-21111000000000000000000000000000
χ424444-2-2-2-2-2-2-2-21444111-2-2-2-2-4-4-2-2-2-2222211111122-1-1-1-1000000000000000000000000000
χ434444-2-2-2-2-2-2-2-214-4-4111-2-2220022-22−2i32i3−2i32i3-1-111-1-100i3−i3i3−i3000000000000000000000000000
χ444444-2-2-2-2-2-2-2-214-4-4111-2-2220022-222i3−2i32i3−2i3-1-111-1-100−i3i3−i3i3000000000000000000000000000
χ454444-2-2-2-2-2-2-2-21-44-411122-2-200222-2−2i32i32i3−2i3-1-1-1-11100i3−i3−i3i3000000000000000000000000000
χ464444-2-2-2-2-2-2-2-21-44-411122-2-200222-22i3−2i3−2i32i3-1-1-1-11100−i3i3i3−i3000000000000000000000000000
χ474444-2-2-2-2-2-2-2-21-4-4411122224-4-2-222-2-22211-1-1-1-1-2211-1-1000000000000000000000000000
χ484444-2-2-2-2-2-2-2-21-4-441112222-44-2-22222-2-211-1-1-1-12-2-1-111000000000000000000000000000
χ4944-4-44444-4-4-4-440004-4-4000000000000000000000000000000000000000000000000002-20
χ5044-4-44444-4-4-4-440004-4-400000000000000000000000000000000000000000000000000-220
χ514-44-444-4-44-44-44000-44-40000000000000000000000000000000000002i−2i000000002i−2i2i−2i000
χ524-44-444-4-44-44-44000-44-4000000000000000000000000000000000000−2i2i00000000−2i2i−2i2i000
χ534-44-4-242-4-224-4-20002-220023−230000000000000023−2300000000000000002i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000
χ544-44-4-242-4-224-4-20002-220023−230000000000000023−230000000000000000−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000
χ554-44-4-242-4-224-4-20002-2200−232300000000000000−232300000000000000002i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000
χ564-44-4-242-4-224-4-20002-2200−232300000000000000−23230000000000000000−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000
χ574-4-4444-4-4-44-444000-4-4400000000000000000000000000000000002-20000002-22-20000000
χ584-4-4444-4-4-44-444000-4-440000000000000000000000000000000000-22000000-22-220000000
χ594-4-44-242-42-2-44-200022-223−230000000000000023−2300000000000000002-2000000−1+31−3−1−31+30000000
χ604-4-44-242-42-2-44-200022-223−230000000000000023−230000000000000000-220000001−3−1+31+3−1−30000000
χ614-4-44-242-42-2-44-200022-2−232300000000000000−232300000000000000002-2000000−1−31+3−1+31−30000000
χ624-4-44-242-42-2-44-200022-2−232300000000000000−23230000000000000000-220000001+3−1−31−3−1+30000000
χ6388-8-88-48-4-8-844-4000-44400000000000000000000000000000000000000000000000000000
χ6488-8-8-48-4844-8-8-4000-44400000000000000000000000000000000000000000000000000000
χ6588-8-8-4-4-4-4444420002-2-2000000000000006-60000000000000000000000000000000000000
χ6688-8-8-4-4-4-4444420002-2-200000000000000-660000000000000000000000000000000000000
χ678-88-88-4-848-8-44-40004-4400000000000000000000000000000000000000000000000000000
χ688-88-8-4-444-44-442000-22-20043−4300000000000000−2323000000000000000000000000000000000
χ698-88-8-4-444-44-442000-22-200−43430000000000000023−23000000000000000000000000000000000
χ708-8-888-4-84-884-4-400044-400000000000000000000000000000000000000000000000000000
χ718-8-88-4-4444-44-42000-2-2243−4300000000000000−232300000000000000000000000000000000000
χ728-8-88-4-4444-44-42000-2-22−43430000000000000023−2300000000000000000000000000000000000

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