Finite Group Databasebeta

← Group #11771808

Character table — Group #11771808

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1111222222222244444444444444444444444488888888888888888888824242424242424242424242424242424242424242424242472727272
order1222223366666622344666666666666666121212124666666121212121212121212121212121244448888121212121212121224242424242424244444
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
χ511111111111111-1-11-1-11111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ611111111111111-1-11-1-11111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-1-111
χ711111111111111-1-11-1-11111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111
χ811111111111111-1-11-1-11111-1-11111111-1-1-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ922222222222222222-2-2222222222222222-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000
χ1022222222222222-2-22222222-2-22222222-2-22222-2-2-2-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000
χ112222222-12-122-1-122-12222-1-122-1-1-1-1-1-1-122-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-10000
χ122222222-12-122-1-122-12222-1-122-1-1-1-1-1-1-122-1-1-1-12-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000-2-2-2-200000000111111110000
χ132222222-12-122-1-122-1-2-222-1-122-1-1-1-1-1-1-1221111-2-1-1-1-1-1-1-2-211-2-211111111000000000000000033−3−333−3−30000
χ142222222-12-122-1-122-1-2-222-1-122-1-1-1-1-1-1-1221111-2-1-1-1-1-1-1-2-211-2-2111111110000000000000000−3−333−3−3330000
χ152222222-12-122-1-1-2-2-12222-1-1-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1-2111111-2-211221111-1-1-1-10000000000000000−i3−i3i3i3i3i3−i3−i30000
χ162222222-12-122-1-1-2-2-12222-1-1-2-2-1-1-1-1-1-1-1-2-2-1-1-1-1-2111111-2-211221111-1-1-1-10000000000000000i3i3−i3−i3−i3−i3i3i30000
χ172222222-12-122-1-1-2-2-1-2-222-1-1-2-2-1-1-1-1-1-1-1-2-21111211111122-1-1-2-2-1-1-1-1111100002i2i−2i−2i00000000−i−i−i−iiiii0000
χ182222222-12-122-1-1-2-2-1-2-222-1-1-2-2-1-1-1-1-1-1-1-2-21111211111122-1-1-2-2-1-1-1-111110000−2i−2i2i2i00000000iiii−i−i−i−i0000
χ19222222-12-12-1-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-122220000-1-1-1-1-1-1-1-1000000000000
χ20222222-12-12-1-12222-122-1-122-1-1-1-1-1-1-1-1-1-1-12222222-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-2000011111111000000000000
χ21222222-12-12-1-12222-1-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-111-2-2111111111100000000−i3−i3i3i3−i3−i3i3i3000000000000
χ22222222-12-12-1-12222-1-2-2-1-122-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-222-1-1-1-111-2-2111111111100000000i3i3−i3−i3i3i3−i3−i3000000000000
χ23222222-12-12-1-122-2-2-122-1-12211-1-1-1-1-1-1-1112222-2-2-2111111-2-2-1-11111-1-1-1-10000000033−3−3−3−333000000000000
χ24222222-12-12-1-122-2-2-122-1-12211-1-1-1-1-1-1-1112222-2-2-2111111-2-2-1-11111-1-1-1-100000000−3−33333−3−3000000000000
χ25222222-12-12-1-122-2-2-1-2-2-1-12211-1-1-1-1-1-1-111-2-2-2-22-2-21111-1-12211-1-1-1-111112i2i−2i−2i0000−i−i−i−iiiii000000000000
χ26222222-12-12-1-122-2-2-1-2-2-1-12211-1-1-1-1-1-1-111-2-2-2-22-2-21111-1-12211-1-1-1-11111−2i−2i2i2i0000iiii−i−i−i−i000000000000
χ272-2-222-22222-2-2-2-20022i−2i2-22-200222-2-2-2-2002i2i−2i−2i000000000002i−2i00002i2i−2i−2i1+i−1−i1−i−1+i00001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ282-2-222-22222-2-2-2-20022i−2i2-22-200222-2-2-2-2002i2i−2i−2i000000000002i−2i00002i2i−2i−2i−1−i1+i−1+i1−i0000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ292-2-222-22222-2-2-2-2002−2i2i2-22-200222-2-2-2-200−2i−2i2i2i00000000000−2i2i0000−2i−2i2i2i1−i−1+i1+i−1−i00001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ302-2-222-22222-2-2-2-2002−2i2i2-22-200222-2-2-2-200−2i−2i2i2i00000000000−2i2i0000−2i−2i2i2i−1+i1−i−1−i1+i0000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ312-2-222-2-12-1211-2-200-12i−2i-112-2−i3i3-1-1-11111−i3i32i2i−2i−2i000−i3−i3i3i33−300−ii33−3−3−i−iii1+i−1−i1−i−1+i0000−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22000000000000
χ322-2-222-2-12-1211-2-200-12i−2i-112-2−i3i3-1-1-11111−i3i32i2i−2i−2i000−i3−i3i3i33−300−ii33−3−3−i−iii−1−i1+i−1+i1−i0000ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22000000000000
χ332-2-222-2-12-1211-2-200-12i−2i-112-2i3−i3-1-1-11111i3−i32i2i−2i−2i000i3i3−i3−i3−3300−ii−3−333−i−iii1+i−1−i1−i−1+i0000−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14000000000000
χ342-2-222-2-12-1211-2-200-12i−2i-112-2i3−i3-1-1-11111i3−i32i2i−2i−2i000i3i3−i3−i3−3300−ii−3−333−i−iii−1−i1+i−1+i1−i0000ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14000000000000
χ352-2-222-2-12-1211-2-200-1−2i2i-112-2−i3i3-1-1-11111−i3i3−2i−2i2i2i000−i3−i3i3i3−3300i−i−3−333ii−i−i1−i−1+i1+i−1−i0000−ζ4−ζ14ζ4+ζ14−ζ20−ζ22ζ20+ζ22−ζ4+ζ14ζ4−ζ14−ζ20+ζ22ζ20−ζ22000000000000
χ362-2-222-2-12-1211-2-200-1−2i2i-112-2−i3i3-1-1-11111−i3i3−2i−2i2i2i000−i3−i3i3i3−3300i−i−3−333ii−i−i−1+i1−i−1−i1+i0000ζ4+ζ14−ζ4−ζ14ζ20+ζ22−ζ20−ζ22ζ4−ζ14−ζ4+ζ14ζ20−ζ22−ζ20+ζ22000000000000
χ372-2-222-2-12-1211-2-200-1−2i2i-112-2i3−i3-1-1-11111i3−i3−2i−2i2i2i000i3i3−i3−i33−300i−i33−3−3ii−i−i1−i−1+i1+i−1−i0000−ζ20−ζ22ζ20+ζ22−ζ4−ζ14ζ4+ζ14−ζ20+ζ22ζ20−ζ22−ζ4+ζ14ζ4−ζ14000000000000
χ382-2-222-2-12-1211-2-200-1−2i2i-112-2i3−i3-1-1-11111i3−i3−2i−2i2i2i000i3i3−i3−i33−300i−i33−3−3ii−i−i−1+i1−i−1−i1+i0000ζ20+ζ22−ζ20−ζ22ζ4+ζ14−ζ4−ζ14ζ20−ζ22−ζ20+ζ22ζ4−ζ14−ζ4+ζ14000000000000
χ392-2-22-222222-2-2-2-22-2200-22-22222-2-222-2-2-2-2000002-22-22-2000000000000000000−i2i2−i2i200000000−i2i2−i2i2−i2i2−i2i20000
χ402-2-22-222222-2-2-2-22-2200-22-22222-2-222-2-2-2-2000002-22-22-2000000000000000000i2−i2i2−i200000000i2−i2i2−i2i2−i2i2−i20000
χ412-2-22-222222-2-2-2-2-22200-22-22-2-22-2-222-2-22200000-22-22-220000000000000000002−2−22000000002−22−2−22−220000
χ422-2-22-222222-2-2-2-2-22200-22-22-2-22-2-222-2-22200000-22-22-22000000000000000000−222−200000000−22−222−22−20000
χ432-2-22-222-12-1-2-2112-2-100-221-122-111-1-111-2-23−33−30-11-11-11003−3003−33−33−33−30000−i2i2−i2i200000000ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000
χ442-2-22-222-12-1-2-2112-2-100-221-122-111-1-111-2-23−33−30-11-11-11003−3003−33−33−33−30000i2−i2i2−i200000000−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000
χ452-2-22-222-12-1-2-2112-2-100-221-122-111-1-111-2-2−33−330-11-11-1100−3300−33−33−33−330000−i2i2−i2i200000000ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000
χ462-2-22-222-12-1-2-2112-2-100-221-122-111-1-111-2-2−33−330-11-11-1100−3300−33−33−33−330000i2−i2i2−i200000000−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000
χ472-2-22-222-12-1-2-211-22-100-221-1-2-2-111-1-111223−33−301-11-11-100−3300−33−333−33−300002−2−2200000000ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000
χ482-2-22-222-12-1-2-211-22-100-221-1-2-2-111-1-111223−33−301-11-11-100−3300−33−333−33−30000−222−200000000−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000
χ492-2-22-222-12-1-2-211-22-100-221-1-2-2-111-1-11122−33−3301-11-11-1003−3003−33−3−33−3300002−2−2200000000ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000
χ502-2-22-222-12-1-2-211-22-100-221-1-2-2-111-1-11122−33−3301-11-11-1003−3003−33−3−33−330000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000
χ51444444-2-2-2-2-2-2-2-244144-2-2-2-2-2-21111111-2-2-2-2-2-24-2-21111-2-2-2-2-2-2111111110000000000000000000000000000
χ52444444-2-2-2-2-2-2-2-2441-4-4-2-2-2-2-2-21111111-2-22222-4-2-21111222222-1-1-1-1-1-1-1-10000000000000000000000000000
χ53444444-2-2-2-2-2-2-2-2-4-4144-2-2-2-222111111122-2-2-2-2-422-1-1-1-12222-2-2-1-1-1-111110000000000000000000000000000
χ54444444-2-2-2-2-2-2-2-2-4-41-4-4-2-2-2-2221111111222222422-1-1-1-1-2-2-2-2221111-1-1-1-10000000000000000000000000000
χ554444-4-44444444400400-4-4-4-4004-4-4-4-4440000000000000000000000000000000000000000000000000000000
χ564444-4-44-24-244-2-200-200-4-42200-22222-2-200−2i32i32i3−2i300000000000000000−2i32i32i3−2i30000000000000000000000000000
χ574444-4-44-24-244-2-200-200-4-42200-22222-2-2002i3−2i3−2i32i3000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ584444-4-4-24-24-2-24400-20022-4-4−2i32i3-22222-2-22i3−2i30000000−2i32i32i3−2i3000000000000000000000000000000000000000000
χ594444-4-4-24-24-2-24400-20022-4-42i3−2i3-22222-2-2−2i32i300000002i3−2i3−2i32i3000000000000000000000000000000000000000000
χ604444-4-4-2-2-2-2-2-2-2-2001002222−2i32i31-1-1-1-1112i3−2i3−2i32i32i3−2i3000i3−i3−i3i3000000-333-3i3−i3−i3i30000000000000000000000000000
χ614444-4-4-2-2-2-2-2-2-2-2001002222−2i32i31-1-1-1-1112i3−2i32i3−2i3−2i32i3000i3−i3−i3i30000003-3-33−i3i3i3−i30000000000000000000000000000
χ624444-4-4-2-2-2-2-2-2-2-20010022222i3−2i31-1-1-1-111−2i32i3−2i32i32i3−2i3000−i3i3i3−i30000003-3-33i3−i3−i3i30000000000000000000000000000
χ634444-4-4-2-2-2-2-2-2-2-20010022222i3−2i31-1-1-1-111−2i32i32i3−2i3−2i32i3000−i3i3i3−i3000000-333-3−i3i3i3−i30000000000000000000000000000
χ6444-4-40044-4-44-44-400400000000-400004-4000000000000000000000000000000000000000000000000000002i−2i
χ6544-4-40044-4-44-44-400400000000-400004-400000000000000000000000000000000000000000000000000000−2i2i
χ664-44-40044-4-4-44-4400400000000-40000-440000000000000000000000000000000000000000000000000002i−2i00
χ674-44-40044-4-4-44-4400400000000-40000-44000000000000000000000000000000000000000000000000000−2i2i00
χ684-4-444-44-24-2-4-42200-24i−4i4-4-2200-2-2-2222200−2i−2i2i2i000000000004i−4i0000−2i−2i2i2i0000000000000000000000000000
χ694-4-444-44-24-2-4-42200-2−4i4i4-4-2200-2-2-22222002i2i−2i−2i00000000000−4i4i00002i2i−2i−2i0000000000000000000000000000
χ704-4-444-4-2-2-2-222220014i−4i-22-22−2i32i3111-1-1-1-1−2i32i3−2i−2i2i2i000i3i3−i3−i323−2300−2i2i−3−333ii−i−i0000000000000000000000000000
χ714-4-444-4-2-2-2-222220014i−4i-22-222i3−2i3111-1-1-1-12i3−2i3−2i−2i2i2i000−i3−i3i3i3−232300−2i2i33−3−3ii−i−i0000000000000000000000000000
χ724-4-444-4-2-2-2-22222001−4i4i-22-22−2i32i3111-1-1-1-1−2i32i32i2i−2i−2i000i3i3−i3−i3−2323002i−2i33−3−3−i−iii0000000000000000000000000000
χ734-4-444-4-2-2-2-22222001−4i4i-22-222i3−2i3111-1-1-1-12i3−2i32i2i−2i−2i000−i3−i3i3i323−23002i−2i−3−333−i−iii0000000000000000000000000000
χ744-4-44-44-24-2422-4-44-4-2002-2-44-2-2-222-2-22222000004-4-22-22000000000000000000000000000000000000000000
χ754-4-44-44-24-2422-4-4-44-2002-2-4422-222-2-222-2-200000-442-22-2000000000000000000000000000000000000000000
χ764-4-44-44-2-2-2-222224-41002-22-2-2-21-1-111-1-12223−2323−230-221-11-10023−2300−33−33−33−330000000000000000000000000000
χ774-4-44-44-2-2-2-222224-41002-22-2-2-21-1-111-1-122−2323−23230-221-11-100−2323003−33−33−33−30000000000000000000000000000
χ784-4-44-44-2-2-2-22222-441002-22-2221-1-111-1-1-2-223−2323−2302-2-11-1100−2323003−33−3−33−330000000000000000000000000000
χ794-4-44-44-2-2-2-22222-441002-22-2221-1-111-1-1-2-2−2323−232302-2-11-110023−2300−33−333−33−30000000000000000000000000000
χ8088-8-8008-4-848-8-4400-40000000040000-440000000000000000000000000000000000000000000000000000000
χ8188-8-800-484-8-448-800-40000000040000-440000000000000000000000000000000000000000000000000000000
χ8288-8-800-4-444-44-4400200000000-26-66-62-20000000000000000000000000000000000000000000000000000000
χ8388-8-800-4-444-44-4400200000000-2-66-662-20000000000000000000000000000000000000000000000000000000
χ848-88-8008-4-84-884-400-400000000400004-40000000000000000000000000000000000000000000000000000000
χ858-88-800-484-84-4-8800-400000000400004-40000000000000000000000000000000000000000000000000000000
χ868-88-800-4-4444-44-400200000000-26-6-66-220000000000000000000000000000000000000000000000000000000
χ878-88-800-4-4444-44-400200000000-2-666-6-220000000000000000000000000000000000000000000000000000000

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