Finite Group Databasebeta

← Group #11778593

Character table — Group #11778593

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order12222233666666344446666666666612121212121212124121212121212121212121212121212121212121244448888121212121212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
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
χ5111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-11-1-1-11111-1-111-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1-1-111-1-1111111-1-1-1-1-1-111
χ8111111111111111-1-11111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22-2-222-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-122-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ122222222-122-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ132222222-122-12-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2-21111-1-1-1-11111111100000000−i3i3−i3i3−i3i3−i3i3000000000000
χ142222222-122-12-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-2-21111-1-1-1-11111111100000000i3−i3i3−i3i3−i3i3−i3000000000000
χ152222222-122-12-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-2-2-1-1111111-1-1-1-111112-22-20000-1-111-1-111000000000000
χ162222222-122-12-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-2-2-1-1111111-1-1-1-11111-22-22000011-1-111-1-1000000000000
χ172222222-122-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-22-2-22211-1-111111111-1-1-1-100000000−i3i3i3−i3−i3i3i3−i3000000000000
χ182222222-122-12-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-22-2-22211-1-111111111-1-1-1-100000000i3−i3−i3i3i3−i3−i3i3000000000000
χ19222222-12-1-12-122-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ20222222-12-1-12-122-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ21222222-12-1-12-122-122-2-2-1-122-1-1-1-1-1-1-122221111-2-1-111-2-2-2-2-1-1-1-111111111000000000000000033−3−333−3−30000
χ22222222-12-1-12-122-122-2-2-1-122-1-1-1-1-1-1-122221111-2-1-111-2-2-2-2-1-1-1-1111111110000000000000000−3−333−3−3330000
χ23222222-12-1-12-122-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2111122-2-21111-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ24222222-12-1-12-122-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2111122-2-21111-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ25222222-12-1-12-122-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-21111211-1-1-2-22211111111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222222-12-1-12-122-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-21111211-1-1-2-22211111111-1-1-1-10000000000000000−3−33333−3−30000
χ272222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-2000002-200000022-2-20000020-20000002200-2-2000000000000
χ282222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-2000002-200000022-2-200000-202000000-2-20022000000000000
χ292222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-22200000-22000000-2-222000020-2000002200-2-200000000000000
χ302222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-22200000-22000000-2-2220000-20200000-2-2002200000000000000
χ312222-2-22-122-12-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-200000-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i3020-20000−i3i3-1-1i3−i311000000000000
χ322222-2-22-122-12-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-200000-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i30-2020000i3−i311−i3i3-1-1000000000000
χ332222-2-22-122-12-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-200000-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i3020-20000i3−i3-1-1−i3i311000000000000
χ342222-2-22-122-12-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-200000-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i30-2020000−i3i311i3−i3-1-1000000000000
χ352222-2-22-122-12-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-222000001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i320-200000-1-1−i3i311i3−i3000000000000
χ362222-2-22-122-12-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-222000001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i3-2020000011i3−i3-1-1−i3i3000000000000
χ372222-2-22-122-12-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-222000001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i320-200000-1-1i3−i311−i3i3000000000000
χ382222-2-22-122-12-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-222000001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i3-2020000011−i3i3-1-1i3−i3000000000000
χ392-2-22-2222-222-2-2-222-2002-22-2-222-2-22-22-22-2000002-20000002-22-2000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-22-2222-222-2-2-222-2002-22-2-222-2-22-22-22-2000002-20000002-22-2000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-22-2222-222-2-2-22-22002-22-2-222-2-22-2-22-2200000-22000000-22-22000000000000−i2i2i2−i200000000−i2i2−i2i2i2−i2i2−i20000
χ422-2-22-2222-222-2-2-22-22002-22-2-222-2-22-2-22-2200000-22000000-22-22000000000000i2−i2−i2i200000000i2−i2i2−i2−i2i2−i2i20000
χ432-2-22-22-121-121-2-2-12-200-112-21-1-111-112-22-23−33−30-113−30000-11-113−33−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ442-2-22-22-121-121-2-2-12-200-112-21-1-111-112-22-23−33−30-113−30000-11-113−33−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ452-2-22-22-121-121-2-2-12-200-112-21-1-111-112-22-2−33−330-11−330000-11-11−33−33−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ462-2-22-22-121-121-2-2-12-200-112-21-1-111-112-22-2−33−330-11−330000-11-11−33−33−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ472-2-22-22-121-121-2-2-1-2200-112-21-1-111-11-22-223−33−301-1−3300001-11-13−33−3−33−330000−i2i2i2−i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ482-2-22-22-121-121-2-2-1-2200-112-21-1-111-11-22-223−33−301-1−3300001-11-13−33−3−33−330000i2−i2−i2i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ492-2-22-22-121-121-2-2-1-2200-112-21-1-111-11-22-22−33−3301-13−300001-11-1−33−333−33−30000−i2i2i2−i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ502-2-22-22-121-121-2-2-1-2200-112-21-1-111-11-22-22−33−3301-13−300001-11-1−33−333−33−30000i2−i2−i2i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
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
χ52444444-2-2-2-2-2-2-2-2144-4-4-2-2-2-21111111-2-2-2-22222-4-2-22222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-21-4-444-2-2-2-211111112222-2-2-2-2-42222-2-222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2-2111111122222222422-2-222-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ554444-4-4-24-2-24-244-2004-422-4-4-22222-2-20000-2-222000004-4000000-2-22200000000000000000000000000000000
χ564444-4-4-24-2-24-244-200-4422-4-4-22222-2-2000022-2-200000-4400000022-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-111−2i3−2i32i32i3-2-22200000-22−2i32i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-1112i32i3−2i3−2i3-2-22200000-222i3−2i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-111−2i3−2i32i32i322-2-2000002-22i3−2i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-1112i32i3−2i3−2i322-2-2000002-2−2i32i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ6144-4-400444-4-4-44-440000000040000-4-400000000000000000000000000000000000000000000000000000002-2
χ6244-4-400444-4-4-44-440000000040000-4-40000000000000000000000000000000000000000000000000000000-22
χ634-44-40044-4-4-44-44400000000-40000-44000000000000000000000000000000000000000000000000000002i−2i00
χ644-44-40044-4-4-44-44400000000-40000-4400000000000000000000000000000000000000000000000000000−2i2i00
χ654-4-444-444-444-4-4-440000-44-44-4-4-4444-4000000000000000000000000000000000000000000000000000000000
χ664-4-444-44-2-44-2-422-20000-442-2222-2-2-22−2i32i32i3−2i30000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ674-4-444-44-2-44-2-422-20000-442-2222-2-2-222i3−2i3−2i32i300000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ684-4-444-4-242-242-4-4-200002-2-44222-2-2-22000023−23−2323000000000000023−23−232300000000000000000000000000000000
χ694-4-444-4-242-242-4-4-200002-2-44222-2-2-220000−232323−230000000000000−232323−2300000000000000000000000000000000
χ704-4-444-4-2-22-2-2222100002-22-2-1-1-1111-1−2i32i32i3−2i323−23−2323000000000i3−i3−i3i3−333−3−3i3i3i−3i0000000000000000000000000000
χ714-4-444-4-2-22-2-2222100002-22-2-1-1-1111-1−2i32i32i3−2i3−232323−23000000000i3−i3−i3i33−3−333i−3i−3i3i0000000000000000000000000000
χ724-4-444-4-2-22-2-2222100002-22-2-1-1-1111-12i3−2i3−2i32i323−23−2323000000000−i3i3i3−i3−333−33i−3i−3i3i0000000000000000000000000000
χ734-4-444-4-2-22-2-2222100002-22-2-1-1-1111-12i3−2i3−2i32i3−232323−23000000000−i3i3i3−i33−3−33−3i3i3i−3i0000000000000000000000000000
χ744-4-44-444-2-44-2-422-24-4004-4-222-2-222-22-22-22000004-4000000-22-22000000000000000000000000000000000000
χ754-4-44-444-2-44-2-422-2-44004-4-222-2-222-222-22-200000-440000002-22-2000000000000000000000000000000000000
χ764-4-44-44-2-22-2-222214-400-22-22-111-1-11-1-22-2223−2323−230-2223−2300001-11-1−33−33−33−330000000000000000000000000000
χ774-4-44-44-2-22-2-222214-400-22-22-111-1-11-1-22-22−2323−23230-22−232300001-11-13−33−33−33−30000000000000000000000000000
χ784-4-44-44-2-22-2-22221-4400-22-22-111-1-11-12-22-223−2323−2302-2−23230000-11-11−33−333−33−30000000000000000000000000000
χ794-4-44-44-2-22-2-22221-4400-22-22-111-1-11-12-22-2−2323−232302-223−230000-11-113−33−3−33−330000000000000000000000000000
χ8088-8-8008-48-84-8-44-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ8188-8-800-48-44-848-8-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-4-4444-4420000000026-66-6-2-2000000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4444-442000000002-66-66-2-2000000000000000000000000000000000000000000000000000000000
χ848-88-8008-4-8-8484-4-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ858-88-800-4844-8-4-88-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4444-44-4200000000-26-6-66-22000000000000000000000000000000000000000000000000000000000
χ878-88-800-4-4444-44-4200000000-2-666-6-22000000000000000000000000000000000000000000000000000000000

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