Finite Group Databasebeta

← Group #13167252

Character table — Group #13167252

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size112224444444444446666668888888888889912121212121212121212121212121216161616181818242424242424242424363636363636727272108108144216
order12346333346666121212226666361212121212121212121222444666666121212121212121212124661212121212121212124881212124242488124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1111-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1111111111-1-11-1
χ411111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-11-1-1111-1-1-111-11
χ5111111111-111111-1-111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1111-1-1-11111-1-1
χ6111111111-111111-1-111111111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111
χ7111111111-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111-11-1-1111-1-1-1111111-1111-1-1-111-1-1-11
χ8111111111-111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111-11-1-1111-1-1-1111111-1-1-11-1-11-1-1111-1
χ922222222222222222000000222222222222-2-20000000000000002222-2-2-2000000000-200-2-2-20000000
χ10222222222-222222-2-200000022222-2-2-2-2-2-22-2-2000000000000000-22-2-2-2-2-2000000000200-2220000000
χ11222-22222202222-20000000022-2-2-2000000-2-2-202-20000000022-2-20-2002-2-2000222-2-2-20002000000000
χ12222-22222202222-20000000022-2-2-2000000-2-2-20-2200000000-2-2220-2002-2-2000-2-2-22220002000000000
χ13222-22222202222-20022222222-2-2-2000000-222-200222222-2-200000-200-222-2-2-2000000000-2000000000
χ14222-22222202222-200-2-2-2-2-2-222-2-2-2000000-222200-2-2-2-2-2-22200000-200-222222000000000-2000000000
χ1522-12-122-1-122-1-12-1-1-100−i3−i3i3i3-1-12-1-122-1-1-1-12-2-200000−i3−i3i3i3−i3i3−i3i3−i3i32-1-1-1-2110−i3i30−i3i30−i3i3-2001110000000
χ1622-12-122-1-122-1-12-1-1-100i3i3−i3−i3-1-12-1-122-1-1-1-12-2-200000i3i3−i3−i3i3−i3i3−i3i3−i32-1-1-1-2110i3−i30i3−i30i3−i3-2001110000000
χ1722-12-122-1-122-1-12-1-1-122-1-1-1-1-1-12-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-12-1-1-12-1-12-1-12-1-12-1-1200-1-1-10000000
χ1822-12-122-1-122-1-12-1-1-1-2-21111-1-12-1-122-1-1-1-1222-2-2-2-2-211111111112-1-1-12-1-1-211-211-211200-1-1-10000000
χ1922-12-122-1-1-22-1-12-11100−i3−i3i3i3-1-12-1-1-2-211112-2-200000−i3−i3i3i3−i3i3i3−i3i3−i3-2-111-2110−i3i30i3−i30i3−i32001-1-10000000
χ2022-12-122-1-1-22-1-12-11100i3i3−i3−i3-1-12-1-1-2-211112-2-200000i3i3−i3−i3i3−i3−i3i3−i3i3-2-111-2110i3−i30−i3i30−i3i32001-1-10000000
χ2122-12-122-1-1-22-1-12-11122-1-1-1-1-1-12-1-1-2-211112222-2-222-1-1-1-1-1-11111-2-1112-1-12-1-1-211-211-200-1110000000
χ2222-12-122-1-1-22-1-12-111-2-21111-1-12-1-1-2-21111222-222-2-2111111-1-1-1-1-2-1112-1-1-2112-1-12-1-1-200-1110000000
χ2322-1-2-122-1-102-1-121−i3i300−i3−i3i3i3-1-1-21100−i3−i3i3i3-2-2-202-200−i3−i3i3i3i3−i3-1-11101−i3i32110i3−i32-1-1-211000-1−i3i30000000
χ2422-1-2-122-1-102-1-121−i3i300i3i3−i3−i3-1-1-21100−i3−i3i3i3-2-2-20-2200i3i3−i3−i3−i3i311-1-101−i3i32110−i3i3-2112-1-1000-1−i3i30000000
χ2522-1-2-122-1-102-1-121−i3i322-1-1-1-1-1-1-21100−i3−i3i3i3-222-20022-1-1-1-111−i3i3i3−i301−i3i3-2-1-1-2110−i3i30i3−i30001i3−i30000000
χ2622-1-2-122-1-102-1-121−i3i3-2-21111-1-1-21100−i3−i3i3i3-222200-2-21111-1-1i3−i3−i3i301−i3i3-2-1-12-1-10i3−i30−i3i30001i3−i30000000
χ2722-1-2-122-1-102-1-121i3−i300−i3−i3i3i3-1-1-21100i3i3−i3−i3-2-2-20-2200−i3−i3i3i3i3−i311-1-101i3−i32110i3−i3-2112-1-1000-1i3−i30000000
χ2822-1-2-122-1-102-1-121i3−i300i3i3−i3−i3-1-1-21100i3i3−i3−i3-2-2-202-200i3i3−i3−i3−i3i3-1-11101i3−i32110−i3i32-1-1-211000-1i3−i30000000
χ2922-1-2-122-1-102-1-121i3−i322-1-1-1-1-1-1-21100i3i3−i3−i3-222-20022-1-1-1-111i3−i3−i3i301i3−i3-2-1-1-2110i3−i30−i3i30001−i3i30000000
χ3022-1-2-122-1-102-1-121i3−i3-2-21111-1-1-21100i3i3−i3−i3-222200-2-21111-1-1−i3i3i3−i301i3−i3-2-1-12-1-10−i3i30i3−i30001−i3i30000000
χ312-220-222220-2-2-2-20002-22-22-22-200000000002-20002-22-22-2000000000002-200000000002−200002−22−200
χ322-220-222220-2-2-2-20002-22-22-22-200000000002-20002-22-22-2000000000002-20000000000−220000−22−2200
χ332-220-222220-2-2-2-2000-22-22-222-200000000002-2000-22-22-22000000000002-200000000002−200002−2−2200
χ342-220-222220-2-2-2-2000-22-22-222-200000000002-2000-22-22-22000000000002-20000000000−220000−222−200
χ35444441-2-2-24-2-2-2144400000011-2-2-2-2-2-2-2-2-210000000000000000011110000000000000220002-1-100-10
χ36444441-2-2-24-2-2-2144400000011-2-2-2-2-2-2-2-2-210000000000000000011110000000000000-2-2000-2110010
χ37444441-2-2-2-4-2-2-214-4-400000011-2-2-2222222100000000000000000-11-1-1000000000000022000-2-1-10010
χ38444441-2-2-2-4-2-2-214-4-400000011-2-2-2222222100000000000000000-11-1-10000000000000-2-200021100-10
χ3944444-21114111-2444222222-2-2111111111-200222-1-1-1-1-1-1222222-2-2-2-2000-1-1-1-1-1-1-1-1-10000000000000
χ4044444-21114111-2444-2-2-2-2-2-2-2-2111111111-200-2-2-2111111-2-2-2-2-2-2-2-2-2-20001111111110000000000000
χ4144444-2111-4111-24-4-4222222-2-2111-1-1-1-1-1-1-2002-2-2-1-1-1-1-1-122-2-2-2-22-222000-1-1-11111110000000000000
χ4244444-2111-4111-24-4-4-2-2-2-2-2-2-2-2111-1-1-1-1-1-1-200-222111111-2-222222-222000111-1-1-1-1-1-10000000000000
χ43444-44-21110111-2-400222222-2-2-1-1-13-33-33-3200-22-2-1-1-1-1-1-1-2-222-2-20200000111-1-1-11110000000000000
χ44444-44-21110111-2-400222222-2-2-1-1-1-33-33-33200-2-22-1-1-1-1-1-1-2-2-2-2220200000111111-1-1-10000000000000
χ45444-44-21110111-2-400-2-2-2-2-2-2-2-2-1-1-13-33-33-32002-2211111122-2-2220200000-1-1-1111-1-1-10000000000000
χ46444-44-21110111-2-400-2-2-2-2-2-2-2-2-1-1-1-33-33-3320022-21111112222-2-20200000-1-1-1-1-1-11110000000000000
χ4744-24-2-21−1−3i32−1+3i3241−1−3i32−1+3i32-2-2-2-222−1−i3−1−i3−1+i3−1+i3111−1−3i32−1+3i3211−1−3i32−1+3i32−1+3i32−1−3i32-200222-1-11+i321+i321−i321−i32−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2111000-11+i321−i32-11+i321−i32-11+i321−i320000000000000
χ4844-24-2-21−1−3i32−1+3i3241−1−3i32−1+3i32-2-2-2-2-2-21+i31+i31−i31−i3111−1−3i32−1+3i3211−1−3i32−1+3i32−1+3i32−1−3i32-200-2-2-211−1−i32−1−i32−1+i32−1+i321+i31−i31+i31−i31+i31−i3-21110001−1−i32−1+i321−1−i32−1+i321−1−i32−1+i320000000000000
χ4944-24-2-21−1−3i32−1+3i32-41−1−3i32−1+3i32-2-22222−1−i3−1−i3−1+i3−1+i3111−1−3i32−1+3i32-1-11+3i321−3i321−3i321+3i32-2002-2-2-1-11+i321+i321−i321−i32−1−i3−1+i31+i31−i31+i31−i321-1-1000-11+i321−i321−1−i32−1+i321−1−i32−1+i320000000000000
χ5044-24-2-21−1−3i32−1+3i32-41−1−3i32−1+3i32-2-222-2-21+i31+i31−i31−i3111−1−3i32−1+3i32-1-11+3i321−3i321−3i321+3i32-200-22211−1−i32−1−i32−1+i32−1+i321+i31−i3−1−i3−1+i3−1−i3−1+i321-1-10001−1−i32−1+i32-11+i321−i32-11+i321−i320000000000000
χ5144-24-2-21−1+3i32−1−3i3241−1+3i32−1−3i32-2-2-2-222−1+i3−1+i3−1−i3−1−i3111−1+3i32−1−3i3211−1+3i32−1−3i32−1−3i32−1+3i32-200222-1-11−i321−i321+i321+i32−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2111000-11−i321+i32-11−i321+i32-11−i321+i320000000000000
χ5244-24-2-21−1+3i32−1−3i3241−1+3i32−1−3i32-2-2-2-2-2-21−i31−i31+i31+i3111−1+3i32−1−3i3211−1+3i32−1−3i32−1−3i32−1+3i32-200-2-2-211−1+i32−1+i32−1−i32−1−i321−i31+i31−i31+i31−i31+i3-21110001−1+i32−1−i321−1+i32−1−i321−1+i32−1−i320000000000000
χ5344-24-2-21−1+3i32−1−3i32-41−1+3i32−1−3i32-2-22222−1+i3−1+i3−1−i3−1−i3111−1+3i32−1−3i32-1-11−3i321+3i321+3i321−3i32-2002-2-2-1-11−i321−i321+i321+i32−1+i3−1−i31−i31+i31−i31+i321-1-1000-11−i321+i321−1+i32−1−i321−1+i32−1−i320000000000000
χ5444-24-2-21−1+3i32−1−3i32-41−1+3i32−1−3i32-2-222-2-21−i31−i31+i31+i3111−1+3i32−1−3i32-1-11−3i321+3i321+3i321−3i32-200-22211−1+i32−1+i32−1−i32−1−i321−i31+i3−1+i3−1−i3−1+i3−1−i321-1-10001−1+i32−1−i32-11−i321+i32-11−i321+i320000000000000
χ5544-2-4-2-21−1−3i32−1+3i3201−1−3i32−1+3i32-22−2i32i322−1−i3−1−i3−1+i3−1+i311-11+3i321−3i323-3−3−i323−i32−3+i323+i32200-22-2-1-11+i321+i321−i321−i321+i31−i3−1−i3−1+i31+i31−i30-1i3−i30001−1−i32−1+i32-11+i321−i321−1−i32−1+i320000000000000
χ5644-2-4-2-21−1−3i32−1+3i3201−1−3i32−1+3i32-22−2i32i3-2-21+i31+i31−i31−i311-11+3i321−3i323-3−3−i323−i32−3+i323+i322002-2211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i31+i31−i3−1−i3−1+i30-1i3−i3000-11+i321−i321−1−i32−1+i32-11+i321−i320000000000000
χ5744-2-4-2-21−1−3i32−1+3i3201−1−3i32−1+3i32-222i3−2i322−1−i3−1−i3−1+i3−1+i311-11+3i321−3i32-333+i32−3+i323−i32−3−i32200-2-22-1-11+i321+i321−i321−i321+i31−i31+i31−i3−1−i3−1+i30-1−i3i30001−1−i32−1+i321−1−i32−1+i32-11+i321−i320000000000000
χ5844-2-4-2-21−1−3i32−1+3i3201−1−3i32−1+3i32-222i3−2i3-2-21+i31+i31−i31−i311-11+3i321−3i32-333+i32−3+i323−i32−3−i3220022-211−1−i32−1−i32−1+i32−1+i32−1−i3−1+i3−1−i3−1+i31+i31−i30-1−i3i3000-11+i321−i32-11+i321−i321−1−i32−1+i320000000000000
χ5944-2-4-2-21−1+3i32−1−3i3201−1+3i32−1−3i32-22−2i32i322−1+i3−1+i3−1−i3−1−i311-11−3i321+3i32-333−i32−3−i323+i32−3+i32200-2-22-1-11−i321−i321+i321+i321−i31+i31−i31+i3−1+i3−1−i30-1i3−i30001−1+i32−1−i321−1+i32−1−i32-11−i321+i320000000000000
χ6044-2-4-2-21−1+3i32−1−3i3201−1+3i32−1−3i32-22−2i32i3-2-21−i31−i31+i31+i311-11−3i321+3i32-333−i32−3−i323+i32−3+i3220022-211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i3−1+i3−1−i31−i31+i30-1i3−i3000-11−i321+i32-11−i321+i321−1+i32−1−i320000000000000
χ6144-2-4-2-21−1+3i32−1−3i3201−1+3i32−1−3i32-222i3−2i322−1+i3−1+i3−1−i3−1−i311-11−3i321+3i323-3−3+i323+i32−3−i323−i32200-22-2-1-11−i321−i321+i321+i321−i31+i3−1+i3−1−i31−i31+i30-1−i3i30001−1+i32−1−i32-11−i321+i321−1+i32−1−i320000000000000
χ6244-2-4-2-21−1+3i32−1−3i3201−1+3i32−1−3i32-222i3−2i3-2-21−i31−i31+i31+i311-11−3i321+3i323-3−3+i323+i32−3−i323−i322002-2211−1+i32−1+i32−1−i32−1−i32−1+i3−1−i31−i31+i3−1+i3−1−i30-1−i3i3000-11−i321+i321−1+i32−1−i32-11−i321+i320000000000000
χ634-440-444440-4-4-4-40000000004-40000000000-4400000000000000000000-440000000000000000000000
χ644-4-20244-2-20-422-400000−2i32i32i3−2i3-220000000000-4400000−2i32i32i3−2i3000000000002-20000000000000000000000
χ654-4-20244-2-20-422-4000002i3−2i3−2i32i3-220000000000-44000002i3−2i3−2i32i3000000000002-20000000000000000000000
χ664-4-20244-2-20-422-40004-4-22-22-2200000000004-40004-4-22-2200000000000-220000000000000000000000
χ674-4-20244-2-20-422-4000-442-22-2-2200000000004-4000-442-22-200000000000-220000000000000000000000
χ68888-882-4-4-40-4-4-42-80000000022444000000-2000000000000000000-2000000000000000000000000000
χ6988-48-42-4228-4222-4-4-4000000-1-1-422-4-422222000000000000000002-1-1-10000000000000000000000000
χ7088-48-42-422-8-4222-444000000-1-1-42244-2-2-2-2200000000000000000-2-1110000000000000000000000000
χ7188-4-8-42-4220-42224−4i34i3000000-1-14-2-2002i32i3−2i3−2i3-20000000000000000001−i3i30000000000000000000000000
χ7288-4-8-42-4220-422244i3−4i3000000-1-14-2-200−2i3−2i32i32i3-20000000000000000001i3−i30000000000000000000000000
χ738-880-82-4-4-40444-20000000002-20000000000000000000000000000000000000000000022−220000−220000
χ748-880-82-4-4-40444-20000000002-200000000000000000000000000000000000000000000−222200002−20000
χ758-880-8-42220-2-2-240004-44-44-4-44000000000000000-22-22-2200000000000000000000000000000000000
χ768-880-8-42220-2-2-24000-44-44-44-440000000000000002-22-22-200000000000000000000000000000000000
χ778-8-404-42−1−3i3−1+3i30-21+3i31−3i340004-4−2−2i32+2i3−2+2i32−2i32-2000000000000000-221+i3−1−i31−i3−1+i300000000000000000000000000000000000
χ788-8-404-42−1−3i3−1+3i30-21+3i31−3i34000-442+2i3−2−2i32−2i3−2+2i32-20000000000000002-2−1−i31+i3−1+i31−i300000000000000000000000000000000000
χ798-8-404-42−1+3i3−1−3i30-21−3i31+3i340004-4−2+2i32−2i3−2−2i32+2i32-2000000000000000-221−i3−1+i31+i3−1−i300000000000000000000000000000000000
χ808-8-404-42−1+3i3−1−3i30-21−3i31+3i34000-442−2i3−2+2i32+2i3−2−2i32-20000000000000002-2−1+i31−i3−1−i31+i300000000000000000000000000000000000
χ8116-16-8084-84408-4-4-4000000000-2200000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).