Finite Group Databasebeta

← Group #11778634

Character table — Group #11778634

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222222224444444444444444448888888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666666663444466666666612121212266666666121212121212121212121212121244448888121212121212121224242424242424242444
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
χ51111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-11-1-11
χ61111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-111-1
χ71111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-111-1
χ81111111111111111111-1-1111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-111111-1-11
χ9222222222222222222222-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ102222222222222222222-2-2-2-2222222222-2-2-2-2222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ112222222-122-122-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-122-122-1-1222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-122-122-1-1222-122-2-2-1-1-1-1-1-1-1-1-11111-2-2-2111111-2-222-1-11111-1-1-1-1000000000000000033−3−333−3−30000
χ142222222-122-122-1-1222-122-2-2-1-1-1-1-1-1-1-1-11111-2-2-2111111-2-222-1-11111-1-1-1-10000000000000000−3−333−3−3330000
χ152222222-122-122-1-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211111122-2-211-1-1-1-11111000022-2-200000000-1-1-1-111110000
χ162222222-122-122-1-1222-1-2-222-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211111122-2-211-1-1-1-111110000-2-222000000001111-1-1-1-10000
χ172222222-122-122-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-1-1-1-1-1-1-2-2-2-21111111111000000000000000033−3−3−3−3330000
χ182222222-122-122-1-1222-1-2-2-2-2-1-1-1-1-1-1-1-1-11111222-1-1-1-1-1-1-2-2-2-211111111110000000000000000−3−33333−3−30000
χ19222222-12-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-1-12-1-122-1-1-1-1222222-1-1-1-1-1-1-122222-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-1-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-211-2-2111111-1-1221111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-1-12-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-2-2-2-2-211-2-2111111-1-1221111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-1-12-1-122-1-1-1-1-2-22222-1-1-1-1-1-1-12222-211-2-21111-1-111-2-2-1-1-1-1111122-2-200001111-1-1-1-1000000000000
χ24222222-12-1-12-1-122-1-1-1-1-2-22222-1-1-1-1-1-1-12222-211-2-21111-1-111-2-2-1-1-1-11111-2-2220000-1-1-1-11111000000000000
χ25222222-12-1-12-1-122-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-11111-2-21111111100000000−i3−i3i3i3i3i3−i3−i3000000000000
χ26222222-12-1-12-1-122-1-1-1-1-2-2-2-222-1-1-1-1-1-1-1-2-2-2-22-1-122-1-1-1-11111-2-21111111100000000i3i3−i3−i3−i3−i3i3i3000000000000
χ272222-2-222-2-222222-2-222002-2-2-22-2-2-2-22222-2-20000000002-2000022-2-20000000000000000000000000000200-2
χ282222-2-222-2-222222-2-222002-2-2-22-2-2-2-22222-2-20000000002-2000022-2-20000000000000000000000000000-2002
χ292222-2-222-2-222222-2-22200-22-2-22-2-2-2-222-2-222000000000-220000-2-222000000000000000000000000000002-20
χ302222-2-222-2-222222-2-22200-22-2-22-2-2-2-222-2-222000000000-220000-2-22200000000000000000000000000000-220
χ312-2-222-222222-2-2-2-2-2-2222i−2i002-2222-2-2-2-20000000000000002i−2i2i−2i00002i2i−2i−2i00002−2−i2i2000000002−22−2−i2i2−i2i20000
χ322-2-222-222222-2-2-2-2-2-2222i−2i002-2222-2-2-2-20000000000000002i−2i2i−2i00002i2i−2i−2i0000−22i2−i200000000−22−22i2−i2i2−i20000
χ332-2-222-222222-2-2-2-2-2-222−2i2i002-2222-2-2-2-2000000000000000−2i2i−2i2i0000−2i−2i2i2i00002−2i2−i2000000002−22−2i2−i2i2−i20000
χ342-2-222-222222-2-2-2-2-2-222−2i2i002-2222-2-2-2-2000000000000000−2i2i−2i2i0000−2i−2i2i2i0000−22−i2i200000000−22−22−i2i2−i2i20000
χ352-2-222-22-122-1-2-211-2-22-12i−2i00-11-1-1-111113−33−3000−i3i3−i3−i3i3i3002i−2i−ii3−33−3−i−iii00002−2−i2i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ362-2-222-22-122-1-2-211-2-22-12i−2i00-11-1-1-111113−33−3000−i3i3−i3−i3i3i3002i−2i−ii3−33−3−i−iii0000−22i2−i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ372-2-222-22-122-1-2-211-2-22-12i−2i00-11-1-1-11111−33−33000i3−i3i3i3−i3−i3002i−2i−ii−33−33−i−iii00002−2−i2i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ382-2-222-22-122-1-2-211-2-22-12i−2i00-11-1-1-11111−33−33000i3−i3i3i3−i3−i3002i−2i−ii−33−33−i−iii0000−22i2−i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ392-2-222-22-122-1-2-211-2-22-1−2i2i00-11-1-1-111113−33−3000i3−i3i3i3−i3−i300−2i2ii−i3−33−3ii−i−i00002−2i2−i200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ402-2-222-22-122-1-2-211-2-22-1−2i2i00-11-1-1-111113−33−3000i3−i3i3i3−i3−i300−2i2ii−i3−33−3ii−i−i0000−22−i2i200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ412-2-222-22-122-1-2-211-2-22-1−2i2i00-11-1-1-11111−33−33000−i3i3−i3−i3i3i300−2i2ii−i−33−33ii−i−i00002−2i2−i200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ422-2-222-22-122-1-2-211-2-22-1−2i2i00-11-1-1-11111−33−33000−i3i3−i3−i3i3i300−2i2ii−i−33−33ii−i−i0000−22−i2i200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ43444444-2-2-2-2-2-2-2-2-2-2-2-214444-2-21111111-2-2-2-24-2-2-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ44444444-2-2-2-2-2-2-2-2-2-2-2-2144-4-4-2-211111112222-42222-1-1-1-122-2-2-2-2-1-1-1-111110000000000000000000000000000
χ45444444-2-2-2-2-2-2-2-2-2-2-2-21-4-444-2-21111111-2-2-2-2-42222-1-1-1-1-2-222221111-1-1-1-10000000000000000000000000000
χ46444444-2-2-2-2-2-2-2-2-2-2-2-21-4-4-4-4-2-2111111122224-2-2-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ474444-4-44-2-4-4-244-2-2-4-44-2004-422-22222-2-2-2-2220000000004-40000-2-22200000000000000000000000000000000
χ484444-4-44-2-4-4-244-2-2-4-44-200-4422-22222-2-222-2-2000000000-44000022-2-200000000000000000000000000000000
χ494444-4-4-24224-2-24422-2-2004-4-4-4-22222-2-244-4-4000000000-220000-2-22200000000000000000000000000000000
χ504444-4-4-24224-2-24422-2-200-44-4-4-22222-2-2-4-4440000000002-2000022-2-200000000000000000000000000000000
χ514444-4-4-2-222-2-2-2-2-222-21004-4221-1-1-1-111-2-222000003-33-3-22000011-1-13-33-30000000000000000000000000000
χ524444-4-4-2-222-2-2-2-2-222-21004-4221-1-1-1-111-2-22200000-33-33-22000011-1-1-33-330000000000000000000000000000
χ534444-4-4-2-222-2-2-2-2-222-2100-44221-1-1-1-11122-2-2000003-33-32-20000-1-111-33-330000000000000000000000000000
χ544444-4-4-2-222-2-2-2-2-222-2100-44221-1-1-1-11122-2-200000-33-332-20000-1-1113-33-30000000000000000000000000000
χ5544-4-4004400-44-44-400-44000000-400004-4000000000000000000000000000002i−2i00002i−2i2i−2i0000000000000000
χ5644-4-4004400-44-44-400-44000000-400004-400000000000000000000000000000−2i2i0000−2i2i−2i2i0000000000000000
χ5744-4-400-24−2i32i3-4-224-4−2i32i32-20000002−2i32i3−2i32i3-22000000000000000000000000000002i−2i00002ζ14−2ζ142ζ22−2ζ220000000000000000
χ5844-4-400-24−2i32i3-4-224-4−2i32i32-20000002−2i32i3−2i32i3-2200000000000000000000000000000−2i2i0000−2ζ142ζ14−2ζ222ζ220000000000000000
χ5944-4-400-242i3−2i3-4-224-42i3−2i32-200000022i3−2i32i3−2i3-22000000000000000000000000000002i−2i00002ζ22−2ζ222ζ14−2ζ140000000000000000
χ6044-4-400-242i3−2i3-4-224-42i3−2i32-200000022i3−2i32i3−2i3-2200000000000000000000000000000−2i2i0000−2ζ222ζ22−2ζ142ζ140000000000000000
χ614-44-4004400-4-44-4400-44000000-40000-440000000000000000000000000002i−2i00000000002i−2i2i−2i000000000000
χ624-44-4004400-4-44-4400-44000000-40000-44000000000000000000000000000−2i2i0000000000−2i2i−2i2i000000000000
χ634-44-400-24−2i32i3-42-2-442i3−2i32-20000002−2i32i32i3−2i32-20000000000000000000000000002i−2i00000000002ζ14−2ζ142ζ22−2ζ22000000000000
χ644-44-400-24−2i32i3-42-2-442i3−2i32-20000002−2i32i32i3−2i32-2000000000000000000000000000−2i2i0000000000−2ζ142ζ14−2ζ222ζ22000000000000
χ654-44-400-242i3−2i3-42-2-44−2i32i32-200000022i3−2i3−2i32i32-20000000000000000000000000002i−2i00000000002ζ22−2ζ222ζ14−2ζ14000000000000
χ664-44-400-242i3−2i3-42-2-44−2i32i32-200000022i3−2i3−2i32i32-2000000000000000000000000000−2i2i0000000000−2ζ222ζ22−2ζ142ζ14000000000000
χ674-4-444-4-24-2-2422-4-422-2-24i−4i004-4-2-2-22222000000000000000−2i2i4i−4i0000−2i−2i2i2i0000000000000000000000000000
χ684-4-444-4-24-2-2422-4-422-2-2−4i4i004-4-2-2-222220000000000000002i−2i−4i4i00002i2i−2i−2i0000000000000000000000000000
χ694-4-444-4-2-2-2-2-2222222-214i−4i00-22111-1-1-1-123−2323−23000−2i32i3i3i3−i3−i300−2i2i−2i2i−33−33ii−i−i0000000000000000000000000000
χ704-4-444-4-2-2-2-2-2222222-214i−4i00-22111-1-1-1-1−2323−23230002i3−2i3−i3−i3i3i300−2i2i−2i2i3−33−3ii−i−i0000000000000000000000000000
χ714-4-444-4-2-2-2-2-2222222-21−4i4i00-22111-1-1-1-123−2323−230002i3−2i3−i3−i3i3i3002i−2i2i−2i−33−33−i−iii0000000000000000000000000000
χ724-4-444-4-2-2-2-2-2222222-21−4i4i00-22111-1-1-1-1−2323−2323000−2i32i3i3i3−i3−i3002i−2i2i−2i3−33−3−i−iii0000000000000000000000000000
χ734-4-44-4444-4-44-4-4-4-444440000-444-4-444-4-40000000000000000000000000000000000000000000000000000000
χ744-4-44-444-2-4-4-2-4-422444-200002-2-222-2-22223−23−232300000000000000023−23−232300000000000000000000000000000000
χ754-4-44-444-2-4-4-2-4-422444-200002-2-222-2-222−232323−23000000000000000−232323−2300000000000000000000000000000000
χ764-4-44-44-2422422-4-4-2-2-2-20000-44-222-2-22200000−2i32i300−2i32i32i3−2i3000000000000000000000000000000000000000000
χ774-4-44-44-2422422-4-4-2-2-2-20000-44-222-2-222000002i3−2i3002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ784-4-44-44-2-222-22222-2-2-2100002-21-1-111-1-123−23−23230−2i32i300i3−i3−i3i3000000−333−3−3i3i3i−3i0000000000000000000000000000
χ794-4-44-44-2-222-22222-2-2-2100002-21-1-111-1-123−23−232302i3−2i300−i3i3i3−i3000000−333−33i−3i−3i3i0000000000000000000000000000
χ804-4-44-44-2-222-22222-2-2-2100002-21-1-111-1-1−232323−230−2i32i300i3−i3−i3i30000003−3−333i−3i−3i3i0000000000000000000000000000
χ814-4-44-44-2-222-22222-2-2-2100002-21-1-111-1-1−232323−2302i3−2i300−i3i3i3−i30000003−3−33−3i3i3i−3i0000000000000000000000000000
χ8288-8-8008-40048-8-4400-8-400000040000-440000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-4−4i34i34-44-44−4i34i342000000-22i3−2i32i3−2i32-20000000000000000000000000000000000000000000000000000000
χ8488-8-800-4-44i3−4i34-44-444i3−4i342000000-2−2i32i3−2i32i32-20000000000000000000000000000000000000000000000000000000
χ858-88-8008-4004-884-400-8-4000000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4−4i34i344-44-44i3−4i342000000-22i3−2i3−2i32i3-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-44i3−4i344-44-4−4i34i342000000-2−2i32i32i3−2i3-220000000000000000000000000000000000000000000000000000000

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