Finite Group Databasebeta

← Group #11778068

Character table — Group #11778068

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order122222336666663444466666666666121212121212121241212121212121212121212121212121212121212244466888812121212121224242424242424242244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-11111-1-1-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-1111111-1-1-1-1-1-111
χ8111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-11-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ10222222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-2222-2-222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-1222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1000000000000
χ122222222-1222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2110000111111000000000000
χ132222222-1222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-222111111111111-1-1-1-10000−i3i30000−i3i3−i3i3−i3i3000000000000
χ142222222-1222-1-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-222111111111111-1-1-1-10000i3−i30000i3−i3i3−i3i3−i3000000000000
χ152222222-1222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-2-211-1-11111-1-1-1-111112-22-2-1-1000011-1-111000000000000
χ162222222-1222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-2-211-1-11111-1-1-1-11111-22-22110000-1-111-1-1000000000000
χ172222222-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-2222-2-2-1-111-1-1-1-1111111110000−i3i30000i3−i3−i3i3i3−i3000000000000
χ182222222-1222-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-2222-2-2-1-111-1-1-1-1111111110000i3−i30000−i3i3i3−i3−i3i3000000000000
χ19222222-12-1-1-1222-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000002222000000-1-1-1-1-1-1-1-10000
χ20222222-12-1-1-1222-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1000000-2-2-2-2000000111111110000
χ21222222-12-1-1-1222-122-2-2-1-122-1-1-1-1-1-1-122221111-211-1-1-2-2-2-211111111-1-1-1-1000000000000000033−3−333−3−30000
χ22222222-12-1-1-1222-122-2-2-1-122-1-1-1-1-1-1-122221111-211-1-1-2-2-2-211111111-1-1-1-10000000000000000−3−333−3−3330000
χ23222222-12-1-1-1222-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-21111-2-2221111-1-1-1-1111100000022-2-2000000-1-1-1-111110000
χ24222222-12-1-1-1222-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-21111-2-2221111-1-1-1-11111000000-2-2220000001111-1-1-1-10000
χ25222222-12-1-1-1222-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-211112-1-11122-2-2-1-1-1-111111111000000000000000033−3−3−3−3330000
χ26222222-12-1-1-1222-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-211112-1-11122-2-2-1-1-1-1111111110000000000000000−3−33333−3−30000
χ272222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-200000002-2000022-2-20000020-20000002200-2-2000000000000
χ282222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-200000002-2000022-2-200000-202000000-2-20022000000000000
χ292222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-2220000000-220000-2-222000020-2022000000-2-200000000000000
χ302222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-2220000000-220000-2-2220000-2020-2-20000002200000000000000
χ312222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-200000−i3i3-11−i3−i3i3i3-1-111−i3−i3i3i3020-2−i3i30000-1-1i3−i311000000000000
χ322222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-200000−i3i3-11−i3−i3i3i3-1-111−i3−i3i3i30-202i3−i3000011−i3i3-1-1000000000000
χ332222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-200000i3−i3-11i3i3−i3−i3-1-111i3i3−i3−i3020-2i3−i30000-1-1−i3i311000000000000
χ342222-2-22-1222-1-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-200000i3−i3-11i3i3−i3−i3-1-111i3i3−i3−i30-202−i3i3000011i3−i3-1-1000000000000
χ352222-2-22-1222-1-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-22200000i3−i31-1i3i3−i3−i311-1-1−i3−i3i3i320-20-1-10000−i3i311i3−i3000000000000
χ362222-2-22-1222-1-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-22200000i3−i31-1i3i3−i3−i311-1-1−i3−i3i3i3-2020110000i3−i3-1-1−i3i3000000000000
χ372222-2-22-1222-1-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-22200000−i3i31-1−i3−i3i3i311-1-1i3i3−i3−i320-20-1-10000i3−i311−i3i3000000000000
χ382222-2-22-1222-1-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-22200000−i3i31-1−i3−i3i3i311-1-1i3i3−i3−i3-2020110000−i3i3-1-1i3−i3000000000000
χ392-22-22-222-22-2-22-222i−2i002-22-2-222-2-22-22i−2i2i−2i00000002i−2i0000000000002i−2i2i−2i0000002−2−i2i20000002−22−2−i2i2−i2i20000
χ402-22-22-222-22-2-22-222i−2i002-22-2-222-2-22-22i−2i2i−2i00000002i−2i0000000000002i−2i2i−2i000000−22i2−i2000000−22−22i2−i2i2−i20000
χ412-22-22-222-22-2-22-22−2i2i002-22-2-222-2-22-2−2i2i−2i2i0000000−2i2i000000000000−2i2i−2i2i0000002−2i2−i20000002−22−2i2−i2i2−i20000
χ422-22-22-222-22-2-22-22−2i2i002-22-2-222-2-22-2−2i2i−2i2i0000000−2i2i000000000000−2i2i−2i2i000000−22−i2i2000000−22−22−i2i2−i2i20000
χ432-22-22-2-121-11-22-2-12i−2i00-112-21-1-111-112i−2i2i−2i3−33−30−i3i3−ii0000−i3i3−i3i33−33−3−ii−ii0000002−2−i2i2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ442-22-22-2-121-11-22-2-12i−2i00-112-21-1-111-112i−2i2i−2i3−33−30−i3i3−ii0000−i3i3−i3i33−33−3−ii−ii000000−22i2−i2000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ452-22-22-2-121-11-22-2-12i−2i00-112-21-1-111-112i−2i2i−2i−33−330i3−i3−ii0000i3−i3i3−i3−33−33−ii−ii0000002−2−i2i2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ462-22-22-2-121-11-22-2-12i−2i00-112-21-1-111-112i−2i2i−2i−33−330i3−i3−ii0000i3−i3i3−i3−33−33−ii−ii000000−22i2−i2000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ472-22-22-2-121-11-22-2-1−2i2i00-112-21-1-111-11−2i2i−2i2i3−33−30i3−i3i−i0000i3−i3i3−i33−33−3i−ii−i0000002−2i2−i2000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ482-22-22-2-121-11-22-2-1−2i2i00-112-21-1-111-11−2i2i−2i2i3−33−30i3−i3i−i0000i3−i3i3−i33−33−3i−ii−i000000−22−i2i2000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ492-22-22-2-121-11-22-2-1−2i2i00-112-21-1-111-11−2i2i−2i2i−33−330−i3i3i−i0000−i3i3−i3i3−33−33i−ii−i0000002−2i2−i2000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ502-22-22-2-121-11-22-2-1−2i2i00-112-21-1-111-11−2i2i−2i2i−33−330−i3i3i−i0000−i3i3−i3i3−33−33i−ii−i000000−22−i2i2000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ51444444-2-2-2-2-2-2-2-214444-2-2-2-21111111-2-2-2-2-2-2-2-24-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-2144-4-4-2-2-2-21111111-2-2-2-22222-422-2-22222-1-1-1-1-1-1-1-111110000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-21-4-444-2-2-2-211111112222-2-2-2-2-4222222-2-2-1-1-1-11111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2-21111111222222224-2-222-2-2221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ554444-4-4-24-2-2-2444-2004-422-4-4-22222-2-20000-2-22200000004-40000-2-22200000000000000000000000000000000
χ564444-4-4-24-2-2-2444-200-4422-4-4-22222-2-2000022-2-20000000-44000022-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-111−2i3−2i32i32i3-2-22200000−2i32i3-22i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-1112i32i3−2i3−2i3-2-222000002i3−2i3-22−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-111−2i3−2i32i32i322-2-2000002i3−2i32-2−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-1112i32i3−2i3−2i322-2-200000−2i32i32-2i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ6144-4-400444-4-44-4-440000000040000-4-400000000000000000000000000000000000000000000000000000002i−2i
χ6244-4-400444-4-44-4-440000000040000-4-40000000000000000000000000000000000000000000000000000000−2i2i
χ634-44-44-44-2-44-42-22-24i−4i004-4-222-2-222-22−2i2i−2i2i00000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000
χ644-44-44-44-2-44-42-22-2−4i4i004-4-222-2-222-222i−2i2i−2i0000000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000
χ654-44-44-4-2-22-222-2214i−4i00-22-22-111-1-11-1−2i2i−2i2i23−2323−230−2i32i3−2i2i0000i3−i3i3−i3−33−33i−ii−i0000000000000000000000000000
χ664-44-44-4-2-22-222-2214i−4i00-22-22-111-1-11-1−2i2i−2i2i−2323−232302i3−2i3−2i2i0000−i3i3−i3i33−33−3i−ii−i0000000000000000000000000000
χ674-44-44-4-2-22-222-221−4i4i00-22-22-111-1-11-12i−2i2i−2i23−2323−2302i3−2i32i−2i0000−i3i3−i3i3−33−33−ii−ii0000000000000000000000000000
χ684-44-44-4-2-22-222-221−4i4i00-22-22-111-1-11-12i−2i2i−2i−2323−23230−2i32i32i−2i0000i3−i3i3−i33−33−3−ii−ii0000000000000000000000000000
χ694-44-4-4444-44-4-44-440000-44-44-4-4-4444-4000000000000000000000000000000000000000000000000000000000
χ704-44-4-444-2-44-42-22-20000-442-2222-2-2-2223−23−232300000000000000000000023−23−23230000000000000000000000000000
χ714-44-4-444-2-44-42-22-20000-442-2222-2-2-22−232323−23000000000000000000000−232323−230000000000000000000000000000
χ724-44-4-44-242-22-44-4-200002-2-44222-2-2-22000023−23−2323000000000000023−23−232300000000000000000000000000000000
χ734-44-4-44-242-22-44-4-200002-2-44222-2-2-220000−232323−230000000000000−232323−2300000000000000000000000000000000
χ744-44-4-44-2-22-222-22100002-22-2-1-1-1111-123−23−232323−23−2323000000000-333-3−333−3−333−30000000000000000000000000000
χ754-44-4-44-2-22-222-22100002-22-2-1-1-1111-123−23−2323−232323−230000000003-3-333−3−33−333−30000000000000000000000000000
χ764-44-4-44-2-22-222-22100002-22-2-1-1-1111-1−232323−2323−23−23230000000003-3-33−333−33−3−330000000000000000000000000000
χ774-44-4-44-2-22-222-22100002-22-2-1-1-1111-1−232323−23−232323−23000000000-333-33−3−333−3−330000000000000000000000000000
χ784-4-440044-4-44-4-44400000000-40000-44000000000000000000000000000000000000000000000000000002-200
χ794-4-440044-4-44-4-44400000000-40000-4400000000000000000000000000000000000000000000000000000-2200
χ8088-8-8008-48-8-8-444-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ8188-8-800-48-4448-8-8-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-4-444-44420000000026-66-6-2-2000000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-444-4442000000002-66-66-2-2000000000000000000000000000000000000000000000000000000000
χ848-8-88008-4-8-8844-4-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ858-8-8800-4844-4-8-88-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-444-444-4200000000-26-6-66-22000000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444-444-4200000000-2-666-6-22000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.