Finite Group Databasebeta

← Group #11780688

Character table — Group #11780688

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222224444444444488888888888888881616161616162424242424242424242424242424242424242424242424247272144
order122233666666344466612121212246612121212121212121212121266612121224446688881212121212122424242424242424884
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1
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
χ511111111111111111111111-1-1-1-1111-1-11111111-1-1-1-1-1-11-11-11111-1-1-1-111-1-11111-1-1-1-111-1
χ611111111111111111111111-1-1-1-1111-1-11111111-1-1-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1-11111-1-11
χ711111111111111111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-11-11-1-111-1-111-1-1111111-1-1-1-1-1-11
χ811111111111111111111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1111111-1
χ922222222222222-2-222222-2-20000-2-2-200222-2-2-2-200000020-2022000000-2-20000000000000
χ1022222222222222-2-222222-2-20000-2-2-200222-2-2-2-2000000-2020-2-2000000220000000000000
χ112222222222222-22-2222-2-22200002-2-200-2-2-222-2-2000000020-20000002200-2-200000000000
χ122222222222222-22-2222-2-22200002-2-200-2-2-222-2-20000000-202000000-2-2002200000000000
χ132222222222222-2-22222-2-2-2-22-222-222-2-2-2-2-2-2-222222-2-2-2000000000000000000000000000
χ142222222222222-2-22222-2-2-2-2-22-2-2-22222-2-2-2-2-222-2-2-2222000000000000000000000000000
χ1522222-122-12-1-1-1222-1-1-1222222-1-1-12-1-1-1-1-1-1-1-1-1-12-1-12-1-12222-1-10000-1-1-1-1-1-100000000000
χ1622222-122-12-1-1-1222-1-1-1222222-1-1-12-1-1-1-1-1-1-1-1-1-12-1-12-1-1-2-2-2-211000011111100000000000
χ1722222-122-12-1-1-1222-1-1-12222-2-211-12-111-1-1-1-1-1-1-1-211-2112-22-2-1-1000011-1-11100000000000
χ1822222-122-12-1-1-1222-1-1-12222-2-211-12-111-1-1-1-1-1-1-1-211-211-22-22110000-1-111-1-100000000000
χ1922222-122-12-1-1-12-2-2-1-1-122-2-200−i3i31-21−i3i3-1-1-111110−i3i30−i3i320-20-1-10000−i3i311−i3i300000000000
χ2022222-122-12-1-1-12-2-2-1-1-122-2-200−i3i31-21−i3i3-1-1-111110−i3i30−i3i3-2020110000i3−i3-1-1i3−i300000000000
χ2122222-122-12-1-1-12-2-2-1-1-122-2-200i3−i31-21i3−i3-1-1-111110i3−i30i3−i320-20-1-10000i3−i311i3−i300000000000
χ2222222-122-12-1-1-12-2-2-1-1-122-2-200i3−i31-21i3−i3-1-1-111110i3−i30i3−i3-2020110000−i3i3-1-1−i3i300000000000
χ2322222-122-12-1-1-1-22-2-1-1-1-2-22200−i3i3-1-21i3−i3111-1-1110−i3i30i3−i3020-2−i3i30000-1-1−i3i31100000000000
χ2422222-122-12-1-1-1-22-2-1-1-1-2-22200−i3i3-1-21i3−i3111-1-1110−i3i30i3−i30-202i3−i3000011i3−i3-1-100000000000
χ2522222-122-12-1-1-1-22-2-1-1-1-2-22200i3−i3-1-21−i3i3111-1-1110i3−i30−i3i3020-2i3−i30000-1-1i3−i31100000000000
χ2622222-122-12-1-1-1-22-2-1-1-1-2-22200i3−i3-1-21−i3i3111-1-1110i3−i30−i3i30-202−i3i3000011−i3i3-1-100000000000
χ2722222-122-12-1-1-1-2-22-1-1-1-2-2-2-22-2-1-112-11111111-1-12-1-1-2110000−i3i30000−i3i3i3−i3i3−i300000000000
χ2822222-122-12-1-1-1-2-22-1-1-1-2-2-2-22-2-1-112-11111111-1-12-1-1-2110000i3−i30000i3−i3−i3i3−i3i300000000000
χ2922222-122-12-1-1-1-2-22-1-1-1-2-2-2-2-221112-1-1-111111-1-1-2112-1-10000−i3i30000i3−i3i3−i3−i3i300000000000
χ3022222-122-12-1-1-1-2-22-1-1-1-2-2-2-2-221112-1-1-111111-1-1-2112-1-10000i3−i30000−i3i3−i3i3i3−i300000000000
χ312222-12-1-12-122-1222-1-1-1-1-1-1-122222-12222-1-1-1-1-1-1-1-1-1-1-1-10000002222000000-1-1-1-1-1-1-1-1000
χ322222-12-1-12-122-1222-1-1-1-1-1-1-122222-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-200000011111111000
χ332222-12-1-12-122-1222-1-1-1-1-1-1-1-2-2-2-22-12-2-22-1-1-1-1-1-111111100000022-2-2000000-1-1-1-11111000
χ342222-12-1-12-122-1222-1-1-1-1-1-1-1-2-2-2-22-12-2-22-1-1-1-1-1-1111111000000-2-2220000001111-1-1-1-1000
χ352222-12-1-12-122-1-2-22-1-1-111112-222-2-12-2-2-21111-1-1-1-1-1111000000000000000033−3−333−3−3000
χ362222-12-1-12-122-1-2-22-1-1-111112-222-2-12-2-2-21111-1-1-1-1-11110000000000000000−3−333−3−333000
χ372222-12-1-12-122-1-2-22-1-1-11111-22-2-2-2-1222-21111-1-1111-1-1-1000000000000000033−3−3−3−333000
χ382222-12-1-12-122-1-2-22-1-1-11111-22-2-2-2-1222-21111-1-1111-1-1-10000000000000000−3−33333−3−3000
χ394444-24-2-24-244-24-4-4-2-2-2-2-2220000-42-4004-2-22222000000000000000000000000000000000
χ404444-24-2-24-244-2-44-4-2-2-222-2-2000042-400-422-2-222000000000000000000000000000000000
χ414444-2-2-2-2-2-2-2-21444111-2-2-2-244-2-2-2-2-2-2-2-2111111-211-211000000000000000000000000000
χ424444-2-2-2-2-2-2-2-21444111-2-2-2-2-4-422-2-2-222-21111112-1-12-1-1000000000000000000000000000
χ434444-2-2-2-2-2-2-2-214-4-4111-2-22200−2i32i3222−2i32i3-211-1-1-1-10i3−i30i3−i3000000000000000000000000000
χ444444-2-2-2-2-2-2-2-214-4-4111-2-222002i3−2i32222i3−2i3-211-1-1-1-10−i3i30−i3i3000000000000000000000000000
χ454444-2-2-2-2-2-2-2-21-44-411122-2-200−2i32i3-2222i3−2i32-1-111-1-10i3−i30−i3i3000000000000000000000000000
χ464444-2-2-2-2-2-2-2-21-44-411122-2-2002i3−2i3-222−2i32i32-1-111-1-10−i3i30i3−i3000000000000000000000000000
χ474444-2-2-2-2-2-2-2-21-4-4411122224-4-2-22-2-2222-1-1-1-111-2112-1-1000000000000000000000000000
χ484444-2-2-2-2-2-2-2-21-4-441112222-44222-2-2-2-22-1-1-1-1112-1-1-211000000000000000000000000000
χ4944-4-444-4-4-444-44000-4-44000000000000000000000000000000000000000000000000002i−2i0
χ5044-4-444-4-4-444-44000-4-4400000000000000000000000000000000000000000000000000−2i2i0
χ514-44-4444-4-4-4-4440004-4-400000000000000000000000000000000002i−2i00000000002i−2i2i−2i000
χ524-44-4444-4-4-4-4440004-4-40000000000000000000000000000000000−2i2i0000000000−2i2i−2i2i000
χ534-44-4-24-22-42-44-2000-2220023−2300000000000023−2300000000000000002i−2i0000000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000
χ544-44-4-24-22-42-44-2000-2220023−2300000000000023−230000000000000000−2i2i0000000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000
χ554-44-4-24-22-42-44-2000-22200−2323000000000000−232300000000000000002i−2i0000000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000
χ564-44-4-24-22-42-44-2000-22200−2323000000000000−23230000000000000000−2i2i0000000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000
χ574-4-4444-444-4-4-44000-44-4000000000000000000000000000000002i−2i000000002i−2i2i−2i0000000
χ584-4-4444-444-4-4-44000-44-400000000000000000000000000000000−2i2i00000000−2i2i−2i2i0000000
χ594-4-44-242-242-4-4-20002-2223−2300000000000023−2300000000000000002i−2i00000000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000000
χ604-4-44-242-242-4-4-20002-2223−2300000000000023−230000000000000000−2i2i00000000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000000
χ614-4-44-242-242-4-4-20002-22−2323000000000000−232300000000000000002i−2i00000000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000000
χ624-4-44-242-242-4-4-20002-22−2323000000000000−23230000000000000000−2i2i00000000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000000
χ6388-8-88-4-8-848-44-400044-400000000000000000000000000000000000000000000000000000
χ6488-8-8-4844-8-48-8-400044-400000000000000000000000000000000000000000000000000000
χ6588-8-8-4-4444-4-442000-2-220000000000000000006-6000000000000000000000000000000000
χ6688-8-8-4-4444-4-442000-2-22000000000000000000-66000000000000000000000000000000000
χ678-88-88-48-84-84-4-4000-44400000000000000000000000000000000000000000000000000000
χ688-88-8-4-4-44444-420002-2-20043−43000000000000−232300000000000000000000000000000000000
χ698-88-8-4-4-44444-420002-2-200−434300000000000023−2300000000000000000000000000000000000
χ708-8-888-4-88-4-844-40004-4400000000000000000000000000000000000000000000000000000
χ718-8-88-4-44-4-44442000-22-243−43000000000000−23230000000000000000000000000000000000000
χ728-8-88-4-44-4-44442000-22-2−434300000000000023−230000000000000000000000000000000000000

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