Finite Group Databasebeta

← Group #11778595

Character table — Group #11778595

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order122222336666666666344446666666661212121241212121212121212121212121212121212121212121244444444121212121212121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
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
χ51111111111111111111-1-111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1111-1-1-1-1-1-1-111-1-1111111-1-111-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-11-111111111-1-1-1-1-1-111-1-1-1-111
χ71111111111111111111-1-111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1111-11-1-1-1-1-1-1-1-1111111-1-111-1-111
χ81111111111111111111-1-111111111111-1-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1-1-11111111-1-111-1-1-1-1-1-11111-1-1
χ9222222222222222222222-2-22222222222222-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-22-2-222-2-2-2-222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ112222222-1222-1222-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1220022000000-1-1-1-10000-1-1-1-10000
χ122222222-1222-1222-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000001111000011110000
χ132222222-1222-1222-12-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2221111-1-1-1-111111111000000000000−i3i3−i3i30000−i3i3−i3i30000
χ142222222-1222-1222-12-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2221111-1-1-1-111111111000000000000i3−i3i3−i30000i3−i3i3−i30000
χ152222222-1222-1222-12-1-1-2-222-1-1-1-1-1-1-1-1-11111-222-2-2-2-2-1-1111111-1-1-1-111112-2002-2000000-1-1110000-1-1110000
χ162222222-1222-1222-12-1-1-2-222-1-1-1-1-1-1-1-1-11111-222-2-2-2-2-1-1111111-1-1-1-11111-2200-2200000011-1-1000011-1-10000
χ172222222-1222-1222-12-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-222-2-211-1-111111111-1-1-1-1000000000000−i3i3i3−i30000−i3i3i3−i30000
χ182222222-1222-1222-12-1-1-2-2-2-2-1-1-1-1-1-1-1-1-111112-2-222-2-211-1-111111111-1-1-1-1000000000000i3−i3−i3i30000i3−i3−i3i30000
χ19222222-12-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100220022-1-1-1-10000-1-1-1-100000000
χ20222222-12-1-1-12-1-1-12-12-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2-211110000111100000000
χ21222222-12-1-1-12-1-1-12-12-122-2-222-1-1-1-1-1-1-12222-21111-1-1-2-2-2-2-1-1-1-11111111100000000−i3−i3i3i30000−i3−i3i3i300000000
χ22222222-12-1-1-12-1-1-12-12-122-2-222-1-1-1-1-1-1-12222-21111-1-1-2-2-2-2-1-1-1-11111111100000000i3i3−i3−i30000i3i3−i3−i300000000
χ23222222-12-1-1-12-1-1-12-12-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-1-1111122-2-21111-1-1-1-11111002200-2-211110000-1-1-1-100000000
χ24222222-12-1-1-12-1-1-12-12-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-2-1-1111122-2-21111-1-1-1-1111100-2-20022-1-1-1-10000111100000000
χ25222222-12-1-1-12-1-1-12-12-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2211-1-111-2-22211111111-1-1-1-100000000−i3−i3i3i30000i3i3−i3−i300000000
χ26222222-12-1-1-12-1-1-12-12-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-2211-1-111-2-22211111111-1-1-1-100000000i3i3−i3−i30000−i3−i3i3i300000000
χ272222-2-2222-2-222-2-22222002-2-2-22-2-2-2-222000002-200002-200000022-2-2000002000-20000000022000000-2-20000
χ282222-2-2222-2-222-2-22222002-2-2-22-2-2-2-222000002-200002-200000022-2-200000-2000200000000-2-2000000220000
χ292222-2-2222-2-222-2-2222200-22-2-22-2-2-2-22200000-220000-22000000-2-22200002000-2000000022000000-2-2000000
χ302222-2-2222-2-222-2-2222200-22-2-22-2-2-2-22200000-220000-22000000-2-2220000-200020000000-2-200000022000000
χ312222-2-22-12-2-2-12-2-2-12-1-1002-211-11111-1-1−i3−i3i3i302-20000-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i302000-2000000−i3i3-1-10000i3−i3110000
χ322222-2-22-12-2-2-12-2-2-12-1-1002-211-11111-1-1−i3−i3i3i302-20000-11−i3i3−i3−i3i3i3-1-111−i3−i3i3i30-20002000000i3−i3110000−i3i3-1-10000
χ332222-2-22-12-2-2-12-2-2-12-1-1002-211-11111-1-1i3i3−i3−i302-20000-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i302000-2000000i3−i3-1-10000−i3i3110000
χ342222-2-22-12-2-2-12-2-2-12-1-1002-211-11111-1-1i3i3−i3−i302-20000-11i3−i3i3i3−i3−i3-1-111i3i3−i3−i30-20002000000−i3i3110000i3−i3-1-10000
χ352222-2-22-12-2-2-12-2-2-12-1-100-2211-11111-1-1−i3−i3i3i30-2200001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i32000-20000000-1-1−i3i3000011i3−i30000
χ362222-2-22-12-2-2-12-2-2-12-1-100-2211-11111-1-1−i3−i3i3i30-2200001-1i3−i3−i3−i3i3i311-1-1i3i3−i3−i3-20002000000011i3−i30000-1-1−i3i30000
χ372222-2-22-12-2-2-12-2-2-12-1-100-2211-11111-1-1i3i3−i3−i30-2200001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i32000-20000000-1-1i3−i3000011−i3i30000
χ382222-2-22-12-2-2-12-2-2-12-1-100-2211-11111-1-1i3i3−i3−i30-2200001-1−i3i3i3i3−i3−i311-1-1−i3−i3i3i3-20002000000011−i3i30000-1-1i3−i30000
χ392-22-2-2222-2-2-22-222-22-222-2002-2-222-2-22-22-22-2000002-200002-22-200000000000000000000000000000000−i2i2−i2i2
χ402-22-2-2222-2-2-22-222-22-222-2002-2-222-2-22-22-22-2000002-200002-22-200000000000000000000000000000000i2−i2i2−i2
χ412-22-2-2222-2-2-22-222-22-22-22002-2-222-2-22-2-22-2200000-220000-22-2200000000000000000000000000000000−i2i2i2−i2
χ422-22-2-2222-2-2-22-222-22-22-22002-2-222-2-22-2-22-2200000-220000-22-2200000000000000000000000000000000i2−i2−i2i2
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-2-2-2-2-2-2-21111111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-21111111-2-2-2-2-42222-2-222221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-4-2-22222-2-222-1-1-1-11111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-211111112222422-2-22222-2-2-1-1-1-1-1-1-1-111110000000000000000000000000000
χ474444-4-4-24-2224-2224-24-2004-4-4-4-22222-2-200000-2200004-4000000-2-22200000000000000000000000000000000
χ484444-4-4-24-2224-2224-24-200-44-4-4-22222-2-2000002-20000-4400000022-2-200000000000000000000000000000000
χ494444-4-4-2-2-222-2-222-2-2-21004-4221-1-1-1-111−2i3−2i32i32i30-220000-22−2i32i3i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-2-222-2-222-2-2-21004-4221-1-1-1-1112i32i3−2i3−2i30-220000-222i3−2i3−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-2-222-2-222-2-2-2100-44221-1-1-1-111−2i3−2i32i32i302-200002-22i3−2i3i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ524444-4-4-2-2-222-2-222-2-2-2100-44221-1-1-1-1112i32i3−2i3−2i302-200002-2−2i32i3−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ5344-4-40044400-4-4004-4-4400000040000-4-40000000000000000000000000000000002-22-22-20000000000000000
χ5444-4-40044400-4-4004-4-4400000040000-4-4000000000000000000000000000000000-22-22-220000000000000000
χ5544-4-400-24-2−2i32i3-42−2i32i342-4-2000000-2−2i32i3−2i32i3220000000000000000000000000000000002-2−1−i31+i3−1+i31−i30000000000000000
χ5644-4-400-24-2−2i32i3-42−2i32i342-4-2000000-2−2i32i3−2i32i322000000000000000000000000000000000-221+i3−1−i31−i3−1+i30000000000000000
χ5744-4-400-24-22i3−2i3-422i3−2i342-4-2000000-22i3−2i32i3−2i3220000000000000000000000000000000002-2−1+i31−i3−1−i31+i30000000000000000
χ5844-4-400-24-22i3−2i3-422i3−2i342-4-2000000-22i3−2i32i3−2i322000000000000000000000000000000000-221−i3−1+i31+i3−1−i30000000000000000
χ594-44-44-444-4444-4-4-4-44-440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ604-44-44-44-2-444-2-4-4-4242-200002-2222-2-2-22−2i32i32i3−2i300000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ614-44-44-44-2-444-2-4-4-4242-200002-2222-2-2-222i3−2i3−2i32i3000000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ624-44-44-4-242-2-24222-4-2-4-20000-44222-2-2-22000000023−230000000000000023−2323−230000000000000000000000000000
χ634-44-44-4-242-2-24222-4-2-4-20000-44222-2-2-220000000−232300000000000000−2323−23230000000000000000000000000000
χ644-44-44-4-2-22-2-2-22222-22100002-2-1-1-1111-1−2i32i32i3−2i300023−23000000i3−i3−i3i33i−3i3i−3i−33−330000000000000000000000000000
χ654-44-44-4-2-22-2-2-22222-22100002-2-1-1-1111-1−2i32i32i3−2i3000−2323000000i3−i3−i3i3−3i3i−3i3i3−33−30000000000000000000000000000
χ664-44-44-4-2-22-2-2-22222-22100002-2-1-1-1111-12i3−2i3−2i32i300023−23000000−i3i3i3−i3−3i3i−3i3i−33−330000000000000000000000000000
χ674-44-44-4-2-22-2-2-22222-22100002-2-1-1-1111-12i3−2i3−2i32i3000−2323000000−i3i3i3−i33i−3i3i−3i3−33−30000000000000000000000000000
χ684-44-4-444-2-4-4-4-2-444242-24-400-222-2-222-22-22-22000004-40000-22-22000000000000000000000000000000000000
χ694-44-4-444-2-4-4-4-2-444242-2-4400-222-2-222-222-22-200000-4400002-22-2000000000000000000000000000000000000
χ704-44-4-44-2422242-2-2-4-2-4-24-4004-42-2-222-224-44-400000-220000-22-22000000000000000000000000000000000000
χ714-44-4-44-2422242-2-2-4-2-4-2-44004-42-2-222-22-44-44000002-200002-22-2000000000000000000000000000000000000
χ724-44-4-44-2-2222-22-2-22-2214-400-22-111-1-11-1-22-2200000-2200001-11-13i−3i−3i3i−3i3i3i−3i0000000000000000000000000000
χ734-44-4-44-2-2222-22-2-22-2214-400-22-111-1-11-1-22-2200000-2200001-11-1−3i3i3i−3i3i−3i−3i3i0000000000000000000000000000
χ744-44-4-44-2-2222-22-2-22-221-4400-22-111-1-11-12-22-2000002-20000-11-113i−3i−3i3i3i−3i−3i3i0000000000000000000000000000
χ754-44-4-44-2-2222-22-2-22-221-4400-22-111-1-11-12-22-2000002-20000-11-11−3i3i3i−3i−3i3i3i−3i0000000000000000000000000000
χ764-4-440044-400-4400-4-444000000-40000-44000000000000000000000000000002i−2i0000000000002i−2i2i−2i00000000
χ774-4-440044-400-4400-4-444000000-40000-4400000000000000000000000000000−2i2i000000000000−2i2i−2i2i00000000
χ784-4-4400-242−2i32i3-4-22i3−2i3-424-200000022i3−2i3−2i32i32-2000000000000000000000000000002i−2i0000000000002ζ14−2ζ142ζ22−2ζ2200000000
χ794-4-4400-242−2i32i3-4-22i3−2i3-424-200000022i3−2i3−2i32i32-200000000000000000000000000000−2i2i000000000000−2ζ142ζ14−2ζ222ζ2200000000
χ804-4-4400-2422i3−2i3-4-2−2i32i3-424-20000002−2i32i32i3−2i32-2000000000000000000000000000002i−2i0000000000002ζ22−2ζ222ζ14−2ζ1400000000
χ814-4-4400-2422i3−2i3-4-2−2i32i3-424-20000002−2i32i32i3−2i32-200000000000000000000000000000−2i2i000000000000−2ζ222ζ22−2ζ142ζ1400000000
χ8288-8-8008-48004-800-4-84-4000000-40000440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4−4i34i344−4i34i3-444200000022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-4-44i3−4i3444i3−4i3-44420000002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ858-8-88008-4-80048004-8-4-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i34-44i3−4i344-42000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i34-4−4i34i344-42000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000

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