Finite Group Databasebeta

← Group #11778070

Character table — Group #11778070

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order122222336666666666344446666666661212121241212121212121212121212121212121212121212121222244444666666121212121212121212128888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
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
χ51111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111-11-1-1-1111111-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-11-11-1-1-1-11111-1-1-1-111-1-111-1-111
χ71111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-11-11111-1-1-1-11111-1-111-1-1-1-111
χ81111111111111111111-1-111111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-11-1111-1-1-1-1-1-1111111-1-11111-1-1
χ9222222222222222222222-2-22222222222222-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-2222-2-2-2-222-2-22222-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-1-1-1-1-1-12-1-122-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12200002200-1-1-1-1-1-1-1-10000000000
χ122222222-1-1-1-1-1-12-1-122-1222222-1-1-1-1-1-1-122222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-2-200111111110000000000
χ132222222-1-1-1-1-1-12-1-122-122-2-222-1-1-1-1-1-1-12222-21111-1-1-2-2-2-211111111-1-1-1-10000000000−i3−i3i3i3−i3−i3i3i30000000000
χ142222222-1-1-1-1-1-12-1-122-122-2-222-1-1-1-1-1-1-12222-21111-1-1-2-2-2-211111111-1-1-1-10000000000i3i3−i3−i3i3i3−i3−i30000000000
χ152222222-1-1-1-1-1-12-1-122-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-111-2-2221111-1-1-1-11111220000-2-200-1-1-1-111110000000000
χ162222222-1-1-1-1-1-12-1-122-1-2-22222-1-1-1-1-1-1-1-2-2-2-2-211-1-111-2-2221111-1-1-1-11111-2-2000022001111-1-1-1-10000000000
χ172222222-1-1-1-1-1-12-1-122-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-1111122-2-2-1-1-1-1111111110000000000−i3−i3i3i3i3i3−i3−i30000000000
χ182222222-1-1-1-1-1-12-1-122-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-1111122-2-2-1-1-1-1111111110000000000i3i3−i3−i3−i3−i3i3i30000000000
χ19222222-1222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100222200-1-100000000-1-1-1-1-1-10000
χ20222222-1222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20011000000001111110000
χ21222222-1222222-122-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222111111111111-1-1-1-100000000−i3i300000000−i3i3−i3i3−i3i30000
χ22222222-1222222-122-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222111111111111-1-1-1-100000000i3−i300000000i3−i3i3−i3i3−i30000
χ23222222-1222222-122-1-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-2-211-1-11111-1-1-1-11111002-22-200-1-10000000011-1-1110000
χ24222222-1222222-122-1-1-1-2-222-1-1-1-1-1-1-1-1-11111-2-2-222-2-211-1-11111-1-1-1-1111100-22-22001100000000-1-111-1-10000
χ25222222-1222222-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-2-2-2-2-1-111-1-1-1-11111111100000000−i3i300000000i3−i3−i3i3i3−i30000
χ26222222-1222222-122-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-2-2-2-2-1-111-1-1-1-11111111100000000i3−i300000000−i3i3i3−i3−i3i30000
χ272222-2-2222-2-2222-2-2222002-2-2-22-2-2-2-22200000002-200002-2000022-2-2000000020-20000000000002200-2-20000
χ282222-2-2222-2-2222-2-2222002-2-2-22-2-2-2-22200000002-200002-2000022-2-20000000-202000000000000-2-200220000
χ292222-2-2222-2-2222-2-222200-22-2-22-2-2-2-2220000000-220000-220000-2-22200000020-2000220000000000-2-2000000
χ302222-2-2222-2-2222-2-222200-22-2-22-2-2-2-2220000000-220000-220000-2-222000000-202000-2-2000000000022000000
χ312222-2-2-122-2-222-1-2-2-1-1-1002-211-11111-1-1−i3−i3i3i30002-200−i3i3-11−i3−i3i3i3-1-111−i3−i3i3i300020-200−i3i300000000-1-1i3−i3110000
χ322222-2-2-122-2-222-1-2-2-1-1-1002-211-11111-1-1−i3−i3i3i30002-200−i3i3-11−i3−i3i3i3-1-111−i3−i3i3i3000-20200i3−i30000000011−i3i3-1-10000
χ332222-2-2-122-2-222-1-2-2-1-1-1002-211-11111-1-1i3i3−i3−i30002-200i3−i3-11i3i3−i3−i3-1-111i3i3−i3−i300020-200i3−i300000000-1-1−i3i3110000
χ342222-2-2-122-2-222-1-2-2-1-1-1002-211-11111-1-1i3i3−i3−i30002-200i3−i3-11i3i3−i3−i3-1-111i3i3−i3−i3000-20200−i3i30000000011i3−i3-1-10000
χ352222-2-2-122-2-222-1-2-2-1-1-100-2211-11111-1-1−i3−i3i3i3000-2200i3−i31-1i3i3−i3−i311-1-1−i3−i3i3i30020-2000-1-100000000−i3i311i3−i30000
χ362222-2-2-122-2-222-1-2-2-1-1-100-2211-11111-1-1−i3−i3i3i3000-2200i3−i31-1i3i3−i3−i311-1-1−i3−i3i3i300-2020001100000000i3−i3-1-1−i3i30000
χ372222-2-2-122-2-222-1-2-2-1-1-100-2211-11111-1-1i3i3−i3−i3000-2200−i3i31-1−i3−i3i3i311-1-1i3i3−i3−i30020-2000-1-100000000i3−i311−i3i30000
χ382222-2-2-122-2-222-1-2-2-1-1-100-2211-11111-1-1i3i3−i3−i3000-2200−i3i31-1−i3−i3i3i311-1-1i3i3−i3−i300-2020001100000000−i3i3-1-1i3−i30000
χ392-22-22-222-2222-2-2-2-22-222i−2i002-2-222-2-22-22i−2i2i−2i000002i−2i0000000000002i−2i2i−2i0000000000000000000000002−2−i2i2
χ402-22-22-222-2222-2-2-2-22-222i−2i002-2-222-2-22-22i−2i2i−2i000002i−2i0000000000002i−2i2i−2i000000000000000000000000−22i2−i2
χ412-22-22-222-2222-2-2-2-22-22−2i2i002-2-222-2-22-2−2i2i−2i2i00000−2i2i000000000000−2i2i−2i2i0000000000000000000000002−2i2−i2
χ422-22-22-222-2222-2-2-2-22-22−2i2i002-2-222-2-22-2−2i2i−2i2i00000−2i2i000000000000−2i2i−2i2i000000000000000000000000−22−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
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-21111111-2-2-2-2-42222-2-22222-1-1-1-1-1-1-1-111110000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-211111112222-422-2-22222-2-2-1-1-1-11111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2111111122224-2-22222-2-2221111-1-1-1-1-1-1-1-10000000000000000000000000000
χ474444-4-44-2-222-2-242244-2004-4-4-4-22222-2-20000000-2200004-40000-2-22200000000000000000000000000000000
χ484444-4-44-2-222-2-242244-200-44-4-4-22222-2-200000002-20000-44000022-2-200000000000000000000000000000000
χ494444-4-4-2-2-222-2-2-222-2-21004-4221-1-1-1-111−2i3−2i32i32i3000-2200−2i32i3-22i3i3−i3−i311-1-1i3i3−i3−i30000000000000000000000000000
χ504444-4-4-2-2-222-2-2-222-2-21004-4221-1-1-1-1112i32i3−2i3−2i3000-22002i3−2i3-22−i3−i3i3i311-1-1−i3−i3i3i30000000000000000000000000000
χ514444-4-4-2-2-222-2-2-222-2-2100-44221-1-1-1-111−2i3−2i32i32i30002-2002i3−2i32-2−i3−i3i3i3-1-111i3i3−i3−i30000000000000000000000000000
χ524444-4-4-2-2-222-2-2-222-2-2100-44221-1-1-1-1112i32i3−2i3−2i30002-200−2i32i32-2i3i3−i3−i3-1-111−i3−i3i3i30000000000000000000000000000
χ5344-4-40044400-4-4400-4-4400000040000-4-40000000000000000000000000000000002i−2i0000002i−2i2i−2i0000000000
χ5444-4-40044400-4-4400-4-4400000040000-4-4000000000000000000000000000000000−2i2i000000−2i2i−2i2i0000000000
χ5544-4-4004-2-2−2i32i3224−2i32i3-4-4-2000000-2−2i32i3−2i32i3220000000000000000000000000000000002i−2i0000002ζ14−2ζ142ζ22−2ζ220000000000
χ5644-4-4004-2-2−2i32i3224−2i32i3-4-4-2000000-2−2i32i3−2i32i322000000000000000000000000000000000−2i2i000000−2ζ142ζ14−2ζ222ζ220000000000
χ5744-4-4004-2-22i3−2i32242i3−2i3-4-4-2000000-22i3−2i32i3−2i3220000000000000000000000000000000002i−2i0000002ζ22−2ζ222ζ14−2ζ140000000000
χ5844-4-4004-2-22i3−2i32242i3−2i3-4-4-2000000-22i3−2i32i3−2i322000000000000000000000000000000000−2i2i000000−2ζ222ζ22−2ζ142ζ140000000000
χ594-44-44-44-22-2-2-22-4224-4-24i−4i004-42-2-222-224i−4i4i−4i00000−2i2i000000000000−2i2i−2i2i0000000000000000000000000000
χ604-44-44-44-22-2-2-22-4224-4-2−4i4i004-42-2-222-22−4i4i−4i4i000002i−2i0000000000002i−2i2i−2i0000000000000000000000000000
χ614-44-44-4-24-4444-42-4-4-22-24i−4i00-222-2-222-22−2i2i−2i2i000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000
χ624-44-44-4-24-4444-42-4-4-22-2−4i4i00-222-2-222-222i−2i2i−2i00000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000
χ634-44-44-4-2-22-2-2-22222-2214i−4i00-22-111-1-11-1−2i2i−2i2i00000−2i2i00003-33-33i−3i3i−3ii−ii−i0000000000000000000000000000
χ644-44-44-4-2-22-2-2-22222-2214i−4i00-22-111-1-11-1−2i2i−2i2i00000−2i2i0000-33-33−3i3i−3i3ii−ii−i0000000000000000000000000000
χ654-44-44-4-2-22-2-2-22222-221−4i4i00-22-111-1-11-12i−2i2i−2i000002i−2i00003-33-3−3i3i−3i3i−ii−ii0000000000000000000000000000
χ664-44-44-4-2-22-2-2-22222-221−4i4i00-22-111-1-11-12i−2i2i−2i000002i−2i0000-33-333i−3i3i−3i−ii−ii0000000000000000000000000000
χ674-44-4-4444-4-4-44-4-4444-440000-44-4-4-4444-40000000000000000000000000000000000000000000000000000000
χ684-44-4-444-2222-22-4-2-24-4-20000-44222-2-2-2200000−2i32i300000000−2i32i32i3−2i3000000000000000000000000000000000000
χ694-44-4-444-2222-22-4-2-24-4-20000-44222-2-2-22000002i3−2i3000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ704-44-4-44-24-4-4-44-4244-22-200002-2222-2-2-2223−23−2323000000000000000000023−23−23230000000000000000000000000000
χ714-44-4-44-24-4-4-44-4244-22-200002-2222-2-2-22−232323−230000000000000000000−232323−230000000000000000000000000000
χ724-44-4-44-2-2222-222-2-2-22100002-2-1-1-1111-123−23−23230−2i32i300000000i3−i3−i3i3−3i3i3i−3i−333−30000000000000000000000000000
χ734-44-4-44-2-2222-222-2-2-22100002-2-1-1-1111-123−23−232302i3−2i300000000−i3i3i3−i33i−3i−3i3i−333−30000000000000000000000000000
χ744-44-4-44-2-2222-222-2-2-22100002-2-1-1-1111-1−232323−230−2i32i300000000i3−i3−i3i33i−3i−3i3i3−3−330000000000000000000000000000
χ754-44-4-44-2-2222-222-2-2-22100002-2-1-1-1111-1−232323−2302i3−2i300000000−i3i3i3−i3−3i3i3i−3i3−3−330000000000000000000000000000
χ764-4-440044-400-44-400-444000000-40000-440000000000000000000000000002-2000000002-22-200000000000000
χ774-4-440044-400-44-400-444000000-40000-44000000000000000000000000000-2200000000-22-2200000000000000
χ784-4-44004-22−2i32i32-2-42i3−2i3-44-20000002−2i32i32i3−2i32-20000000000000000000000000002-200000000−1+i31−i3−1−i31+i300000000000000
χ794-4-44004-22−2i32i32-2-42i3−2i3-44-20000002−2i32i32i3−2i32-2000000000000000000000000000-22000000001−i3−1+i31+i3−1−i300000000000000
χ804-4-44004-222i3−2i32-2-4−2i32i3-44-200000022i3−2i3−2i32i32-20000000000000000000000000002-200000000−1−i31+i3−1+i31−i300000000000000
χ814-4-44004-222i3−2i32-2-4−2i32i3-44-200000022i3−2i3−2i32i32-2000000000000000000000000000-22000000001+i3−1−i31−i3−1+i300000000000000
χ8288-8-800-48800-8-8-40044-4000000-40000440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4-4−4i34i344-4−4i34i344200000022i3−2i32i3−2i3-2-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-4-44i3−4i344-44i3−4i34420000002−2i32i3−2i32i3-2-20000000000000000000000000000000000000000000000000000000
χ858-8-8800-48-800-884004-4-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-8-8800-4-44−4i34i34-444i3−4i34-42000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-8-8800-4-444i3−4i34-44−4i34i34-42000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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