Finite Group Databasebeta

← Group #11778787

Character table — Group #11778787

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666634444666666666661212121212121212412121212121212121212121212121212121212122244666688881212121224242424242424244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
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
χ5111111111111111-1-11111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-111-1-1
χ6111111111111111-1-11111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-1-1-1-11111-1-1-1-1-1-11111-1-111
χ7111111111111111-1-11111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11111-1-1-1-1111111-1-1-1-1-1-111
χ8111111111111111-1-11111111111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-1111111-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ10222222222222222-2-2-2-222222222222-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-12-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-10000-1-1-1-1000000000000
χ122222222-12-122-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100001111000000000000
χ132222222-12-122-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22211-2-211-1-1-1-1111111110000−i3i3−i3i30000−i3i3−i3i3000000000000
χ142222222-12-122-1-1-122-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-22211-2-211-1-1-1-1111111110000i3−i3i3−i30000i3−i3i3−i3000000000000
χ152222222-12-122-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-1-1-2-2111111-1-1-1-111112-22-2-1-1110000-1-111000000000000
χ162222222-12-122-1-1-1-2-22222-1-1-1-1-1-1-1-1-111112222-2-2-2-1-1-2-2111111-1-1-1-11111-22-2211-1-1000011-1-1000000000000
χ172222222-12-122-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-22-2-21122-1-111111111-1-1-1-10000−i3i3i3−i30000−i3i3i3−i3000000000000
χ182222222-12-122-1-1-1-2-2-2-222-1-1-1-1-1-1-1-1-11111-2-2-2-22-2-21122-1-111111111-1-1-1-10000i3−i3−i3i30000i3−i3−i3i3000000000000
χ19222222-12-12-1-122-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-10000000022220000-1-1-1-1-1-1-1-10000
χ20222222-12-12-1-122-12222-1-122-1-1-1-1-1-1-12222-1-1-1-12-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-100000000-2-2-2-20000111111110000
χ21222222-12-12-1-122-122-2-2-1-122-1-1-1-1-1-1-122221111-2-1-1-2-211-2-2-1-1-1-111111111000000000000000033−3−333−3−30000
χ22222222-12-12-1-122-122-2-2-1-122-1-1-1-1-1-1-122221111-2-1-1-2-211-2-2-1-1-1-1111111110000000000000000−3−333−3−3330000
χ23222222-12-12-1-122-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2112211-2-21111-1-1-1-111110000000022-2-20000-1-1-1-111110000
χ24222222-12-12-1-122-1-2-222-1-122-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2112211-2-21111-1-1-1-1111100000000-2-22200001111-1-1-1-10000
χ25222222-12-12-1-122-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-21111211-2-2-1-12211111111-1-1-1-1000000000000000033−3−3−3−3330000
χ26222222-12-12-1-122-1-2-2-2-2-1-122-1-1-1-1-1-1-1-2-2-2-21111211-2-2-1-12211111111-1-1-1-10000000000000000−3−33333−3−30000
χ272222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-20002-20000000022-2-20000020-20022000000-2-2000000000000
χ282222-2-2222222222002-2-2-2-2-22-2-2-2-222000022-2-20002-20000000022-2-200000-20200-2-200000022000000000000
χ292222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-222000-2200000000-2-222000020-2022000000-2-200000000000000
χ302222-2-222222222200-22-2-2-2-22-2-2-2-2220000-2-222000-2200000000-2-2220000-2020-2-20000002200000000000000
χ312222-2-22-12-122-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-2000-1100−i3i3−i3−i3i3i3-1-111−i3−i3i3i3020-2−i3i3-1-10000i3−i311000000000000
χ322222-2-22-12-122-1-1-1002-2-2-211-11111-1-1−i3−i3i3i322-2-2000-1100−i3i3−i3−i3i3i3-1-111−i3−i3i3i30-202i3−i3110000−i3i3-1-1000000000000
χ332222-2-22-12-122-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-2000-1100i3−i3i3i3−i3−i3-1-111i3i3−i3−i3020-2i3−i3-1-10000−i3i311000000000000
χ342222-2-22-12-122-1-1-1002-2-2-211-11111-1-1i3i3−i3−i322-2-2000-1100i3−i3i3i3−i3−i3-1-111i3i3−i3−i30-202−i3i3110000i3−i3-1-1000000000000
χ352222-2-22-12-122-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-2220001-100i3−i3−i3−i3i3i311-1-1i3i3−i3−i320-20-1-1−i3i3000011i3−i3000000000000
χ362222-2-22-12-122-1-1-100-22-2-211-11111-1-1−i3−i3i3i3-2-2220001-100i3−i3−i3−i3i3i311-1-1i3i3−i3−i3-202011i3−i30000-1-1−i3i3000000000000
χ372222-2-22-12-122-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-2220001-100−i3i3i3i3−i3−i311-1-1−i3−i3i3i320-20-1-1i3−i3000011−i3i3000000000000
χ382222-2-22-12-122-1-1-100-22-2-211-11111-1-1i3i3−i3−i3-2-2220001-100−i3i3i3i3−i3−i311-1-1−i3−i3i3i3-202011−i3i30000-1-1i3−i3000000000000
χ392-22-22-222-2-22-2-2222-2002-22-2-222-2-22-22-22-2000002-20000002-22-20000000000000000−i2i2−i2i20000−i2i2−i2i2−i2i2−i2i20000
χ402-22-22-222-2-22-2-2222-2002-22-2-222-2-22-22-22-2000002-20000002-22-20000000000000000i2−i2i2−i20000i2−i2i2−i2i2−i2i2−i20000
χ412-22-22-222-2-22-2-222-22002-22-2-222-2-22-2-22-2200000-22000000-22-220000000000000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i20000
χ422-22-22-222-2-22-2-222-22002-22-2-222-2-22-2-22-2200000-22000000-22-220000000000000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i20000
χ432-22-22-2-121-2-11-22-12-200-112-21-1-111-112-22-23−33−30-11003−300-11-113−33−33−33−300000000−i2i2−i2i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ442-22-22-2-121-2-11-22-12-200-112-21-1-111-112-22-23−33−30-11003−300-11-113−33−33−33−300000000i2−i2i2−i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ452-22-22-2-121-2-11-22-12-200-112-21-1-111-112-22-2−33−330-1100−3300-11-11−33−33−33−3300000000−i2i2−i2i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ462-22-22-2-121-2-11-22-12-200-112-21-1-111-112-22-2−33−330-1100−3300-11-11−33−33−33−3300000000i2−i2i2−i20000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ472-22-22-2-121-2-11-22-1-2200-112-21-1-111-11-22-223−33−301-100−33001-11-13−33−3−33−3300000000−i2i2i2−i20000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ482-22-22-2-121-2-11-22-1-2200-112-21-1-111-11-22-223−33−301-100−33001-11-13−33−3−33−3300000000i2−i2−i2i20000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ492-22-22-2-121-2-11-22-1-2200-112-21-1-111-11-22-22−33−3301-1003−3001-11-1−33−333−33−300000000−i2i2i2−i20000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ502-22-22-2-121-2-11-22-1-2200-112-21-1-111-11-22-22−33−3301-1003−3001-11-1−33−333−33−300000000i2−i2−i2i20000−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
χ53444444-2-2-2-2-2-2-2-21-4-444-2-2-2-211111112222-2-2-2-2-422-2-22222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-21-4-4-4-4-2-2-2-211111112222222242222-2-2-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ554444-4-4-24-24-2-244-2004-422-4-4-22222-2-20000-2-2220004-400000000-2-22200000000000000000000000000000000
χ564444-4-4-24-24-2-244-200-4422-4-4-22222-2-2000022-2-2000-440000000022-2-200000000000000000000000000000000
χ574444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-111−2i3−2i32i32i3-2-222000-2200−2i32i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ584444-4-4-2-2-2-2-2-2-2-21004-422221-1-1-1-1112i32i3−2i3−2i3-2-222000-22002i3−2i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ594444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-111−2i3−2i32i32i322-2-20002-2002i3−2i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2100-4422221-1-1-1-1112i32i3−2i3−2i322-2-20002-200−2i32i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ6144-4-40044-4-4-444-4400000000-40000-44000000000000000000000000000000000000000000000000000002i−2i00
χ6244-4-40044-4-4-444-4400000000-40000-4400000000000000000000000000000000000000000000000000000−2i2i00
χ634-44-44-44-2-424-42-2-24-4004-4-222-2-222-22-22-22000004-4000000-22-22000000000000000000000000000000000000
χ644-44-44-44-2-424-42-2-2-44004-4-222-2-222-222-22-200000-440000002-22-2000000000000000000000000000000000000
χ654-44-44-4-2-222-222-214-400-22-22-111-1-11-1-22-2223−2323−230-220023−23001-11-1−33−33−33−330000000000000000000000000000
χ664-44-44-4-2-222-222-214-400-22-22-111-1-11-1-22-22−2323−23230-2200−2323001-11-13−33−33−33−30000000000000000000000000000
χ674-44-44-4-2-222-222-21-4400-22-22-111-1-11-12-22-223−2323−2302-200−232300-11-11−33−333−33−30000000000000000000000000000
χ684-44-44-4-2-222-222-21-4400-22-22-111-1-11-12-22-2−2323−232302-20023−2300-11-113−33−3−33−330000000000000000000000000000
χ694-44-4-4444-4-44-4-4440000-44-44-4-4-4444-4000000000000000000000000000000000000000000000000000000000
χ704-44-4-444-2-424-42-2-20000-442-2222-2-2-22−2i32i32i3−2i30000000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ714-44-4-444-2-424-42-2-20000-442-2222-2-2-222i3−2i3−2i32i300000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ724-44-4-44-242-4-22-44-200002-2-44222-2-2-22000023−23−2323000000000000023−23−232300000000000000000000000000000000
χ734-44-4-44-242-4-22-44-200002-2-44222-2-2-220000−232323−230000000000000−232323−2300000000000000000000000000000000
χ744-44-4-44-2-222-222-2100002-22-2-1-1-1111-1−2i32i32i3−2i323−23−2323000000000i3−i3−i3i3−333−3−3i3i3i−3i0000000000000000000000000000
χ754-44-4-44-2-222-222-2100002-22-2-1-1-1111-1−2i32i32i3−2i3−232323−23000000000i3−i3−i3i33−3−333i−3i−3i3i0000000000000000000000000000
χ764-44-4-44-2-222-222-2100002-22-2-1-1-1111-12i3−2i3−2i32i323−23−2323000000000−i3i3i3−i3−333−33i−3i−3i3i0000000000000000000000000000
χ774-44-4-44-2-222-222-2100002-22-2-1-1-1111-12i3−2i3−2i32i3−232323−23000000000−i3i3i3−i33−3−33−3i3i3i−3i0000000000000000000000000000
χ784-4-44004444-4-4-4-440000000040000-4-400000000000000000000000000000000000000000000000000000002i−2i
χ794-4-44004444-4-4-4-440000000040000-4-40000000000000000000000000000000000000000000000000000000−2i2i
χ8088-8-8008-4-84-88-44-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ8188-8-800-484-84-48-8-400000000400004-4000000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-4444-4-44200000000-26-66-6-22000000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4444-4-44200000000-2-66-66-22000000000000000000000000000000000000000000000000000000000
χ848-8-88008-48-4-8-844-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ858-8-8800-48-4844-8-8-400000000-4000044000000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-4-4-4444420000000026-6-66-2-2000000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-4-4-444442000000002-666-6-2-2000000000000000000000000000000000000000000000000000000000

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