Finite Group Databasebeta

← Group #10690155

Character table — Group #10690155

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size1111111122222222222244444444444488888888888888888888888888888812121212161616162424242424242424242424242424
order12224444223446661212121222446666121212124444444468888121212121212121212121212121212121222442424242422444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-1ii−i−i11111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−i111-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-1ii−i−i-1ii−i−i11111-1-1-1-1iiii−i−i−i−i-1-111ii−i−i-1-1-1111−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii-1−i−iii11111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii111-1-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-111-1-1−i−iii-1−i−iii11111-1-1-1-1−i−i−i−iiiii-1-111−i−iii-1-1-1111ii−i−iii−i−i
χ131111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-1−i−iii1-1-1-1-11111iiii−i−i−i−i11-1-1−i−iii-1-11-111ii−i−i−i−iii
χ141111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-111ii−i−i-1−i−iii1-1-1-1-11111iiii−i−i−i−i-1-111−i−iii11-11-1-1−i−iiiii−i−i
χ151111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-111−i−iii-1ii−i−i1-1-1-1-11111−i−i−i−iiiii11-1-1ii−i−i-1-11-111−i−iiiii−i−i
χ161111-1-1-1-1111-1-1111-1-1-1-1-1-11111-1-111-1-1-1-111−i−iii-1ii−i−i1-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i11-11-1-1ii−i−i−i−iii
χ1722222222222222222222-2-2-2-222-2-2-2-22200000000-20000-200000000000000002222000000-2-20000000000
χ1822222222222222222222-2-2-2-222-2-2-2-22200000000-20000-20000000000000000-2-2-2-2000000220000000000
χ192222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-100000000000000
χ202222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-2-2-2-2-1-2-2-2-2-1-1-1-1-1-1-1-1-1111111110000111100000000000000
χ212222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-22222-1-2-2-2-2-111111111-1-1-1-1-1-1-1-10000111100000000000000
χ222222222222-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-12222-111111111111111110000-1-1-1-100000000000000
χ2322222222-2-22-2-222222222-22-2-2-22222-2-200000000-20000-200000000000000000000000000000000002-22-2
χ2422222222-2-22-2-222222222-22-2-2-22222-2-200000000-20000-20000000000000000000000000000000000-22-22
χ2522222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-20000000022-22-22000000000000000000002-22-200000000000000
χ2622222222-2-22-2-22222222-22-22-2-2-2-2-2-2-2-2000000002-22-22200000000000000000000-22-2200000000000000
χ2722222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100000000-12-22-2-133−3−333−3−333−3−333−3−30000-11-1100000000000000
χ2822222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100000000-12-22-2-1−3−333−3−333−3−333−3−3330000-11-1100000000000000
χ2922222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100000000-1-22-22-133−3−333−3−3−3−333−3−33300001-11-100000000000000
χ3022222222-2-2-1-2-2-1-1-1-1-1-1-1-22-221111111100000000-1-22-22-1−3−333−3−33333−3−333−3−300001-11-100000000000000
χ312222-2-2-2-2222-2-2222-2-2-2-222-2-22222-2-2-2-20000000020000-2000000000000000022-2-2000000-220000000000
χ322222-2-2-2-2222-2-2222-2-2-2-222-2-22222-2-2-2-20000000020000-20000000000000000-2-2220000002-20000000000
χ332222-2-2-2-222-1-2-2-1-1-11111-2-222-1-111-1-11122-2-22i2i−2i−2i12i2i−2i−2i-1-1-1-1-11111−i−i−i−iiiii0000−i−iii00000000000000
χ342222-2-2-2-222-1-2-2-1-1-11111-2-222-1-111-1-11122-2-2−2i−2i2i2i1−2i−2i2i2i-1-1-1-1-11111iiii−i−i−i−i0000ii−i−i00000000000000
χ352222-2-2-2-222-1-2-2-1-1-11111-2-222-1-111-1-111-2-2222i2i−2i−2i1−2i−2i2i2i-11111-1-1-1-1−i−i−i−iiiii0000ii−i−i00000000000000
χ362222-2-2-2-222-1-2-2-1-1-11111-2-222-1-111-1-111-2-222−2i−2i2i2i12i2i−2i−2i-11111-1-1-1-1iiii−i−i−i−i0000−i−iii00000000000000
χ372222-2-2-2-2-2-2222222-2-2-2-22-2-22-2-222-2-22200000000-22i−2i−2i2i2000000000000000000002i−2i−2i2i00000000000000
χ382222-2-2-2-2-2-2222222-2-2-2-22-2-22-2-222-2-22200000000-2−2i2i2i−2i200000000000000000000−2i2i2i−2i00000000000000
χ392222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-222220000000020000-200000000000000000000000000000000002i−2i−2i2i
χ402222-2-2-2-2-2-2222222-2-2-2-2-222-2-2-2-2-222220000000020000-20000000000000000000000000000000000−2i2i2i−2i
χ412222-2-2-2-2-2-2-122-1-1-111112-2-2211-1-111-1-10000000012i−2i−2i2i-133−3−3−3−333i3i3−i3−i3−i3−i3i3i30000−iii−i00000000000000
χ422222-2-2-2-2-2-2-122-1-1-111112-2-2211-1-111-1-10000000012i−2i−2i2i-1−3−33333−3−3−i3−i3i3i3i3i3−i3−i30000−iii−i00000000000000
χ432222-2-2-2-2-2-2-122-1-1-111112-2-2211-1-111-1-1000000001−2i2i2i−2i-133−3−3−3−333−i3−i3i3i3i3i3−i3−i30000i−i−ii00000000000000
χ442222-2-2-2-2-2-2-122-1-1-111112-2-2211-1-111-1-1000000001−2i2i2i−2i-1−3−33333−3−3i3i3−i3−i3−i3−i3i3i30000i−i−ii00000000000000
χ4522-2-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i00002-200002i−2i00001+i−1−i1−i−1+i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i2-22i−2i00000000001+i−1−i1−i−1+i0000
χ4622-2-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i00002-200002i−2i00001+i−1−i1−i−1+i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i-22−2i2i0000000000−1−i1+i−1+i1−i0000
χ4722-2-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i00002-200002i−2i0000−1−i1+i−1+i1−i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2-22i−2i0000000000−1−i1+i−1+i1−i0000
χ4822-2-22i2i−2i−2i2-222i−2i2-2-22i2i−2i−2i00002-200002i−2i0000−1−i1+i−1+i1−i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i-22−2i2i00000000001+i−1−i1−i−1+i0000
χ4922-2-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i00002-20000−2i2i00001−i−1+i1+i−1−i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i2-2−2i2i00000000001−i−1+i1+i−1−i0000
χ5022-2-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i00002-20000−2i2i00001−i−1+i1+i−1−i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i-222i−2i0000000000−1+i1−i−1−i1+i0000
χ5122-2-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i00002-20000−2i2i0000−1+i1−i−1−i1+i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-2−2i2i0000000000−1+i1−i−1−i1+i0000
χ5222-2-2−2i−2i2i2i2-22−2i2i2-2-2−2i−2i2i2i00002-20000−2i2i0000−1+i1−i−1−i1+i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i-222i−2i00000000001−i−1+i1+i−1−i0000
χ534444444444-244-2-2-2-2-2-2-2-4-4-4-4-2-22222-2-20000000020000200000000000000000000000000000000000000
χ5444444444-4-4-2-4-4-2-2-2-2-2-2-24-44-422-2-2-2-2220000000020000200000000000000000000000000000000000000
χ554444-4-4-4-444-2-4-4-2-2-2222244-4-4-2-2-2-2222200000000-20000200000000000000000000000000000000000000
χ564444-4-4-4-4-4-4-244-2-2-22222-444-42222-2-2-2-200000000-20000200000000000000000000000000000000000000
χ5744-4-44i4i−4i−4i4-4-24i−4i-222−2i−2i2i2i0000-220000−2i2i00002+2i−2−2i2−2i−2+2i00000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000000000
χ5844-4-44i4i−4i−4i4-4-24i−4i-222−2i−2i2i2i0000-220000−2i2i0000−2−2i2+2i−2+2i2−2i000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000000000
χ5944-4-44i4i−4i−4i-444−4i4i4-4-44i4i−4i−4i0000-440000−4i4i0000000000000000000000000000000000000000000000000000
χ6044-4-44i4i−4i−4i-44-2−4i4i-222−2i−2i2i2i00002-200002i−2i0000000000000000000000−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ110000000000000000000000
χ6144-4-44i4i−4i−4i-44-2−4i4i-222−2i−2i2i2i00002-200002i−2i0000000000000000000000ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ110000000000000000000000
χ6244-4-4−4i−4i4i4i4-4-2−4i4i-2222i2i−2i−2i0000-2200002i−2i00002−2i−2+2i2+2i−2−2i00000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000000000
χ6344-4-4−4i−4i4i4i4-4-2−4i4i-2222i2i−2i−2i0000-2200002i−2i0000−2+2i2−2i−2−2i2+2i000000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000000000
χ6444-4-4−4i−4i4i4i-4444i−4i4-4-4−4i−4i4i4i0000-4400004i−4i0000000000000000000000000000000000000000000000000000
χ6544-4-4−4i−4i4i4i-44-24i−4i-2222i2i−2i−2i00002-20000−2i2i0000000000000000000000−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ110000000000000000000000
χ6644-4-4−4i−4i4i4i-44-24i−4i-2222i2i−2i−2i00002-20000−2i2i0000000000000000000000ζ2+ζ7−ζ10−ζ11−ζ2−ζ7+ζ10+ζ11−ζ2−ζ7+ζ10+ζ11ζ2+ζ7−ζ10−ζ11−ζ2+ζ7+ζ10−ζ11ζ2−ζ7−ζ10+ζ11ζ2−ζ7−ζ10+ζ11−ζ2+ζ7+ζ10−ζ110000000000000000000000
χ674-44-44i−4i4i−4i00400-44-44i−4i4i−4i0000000000002-22i−2i00000000002-22-22i−2i2i−2i000000000000000000000000000000
χ684-44-44i−4i4i−4i00400-44-44i−4i4i−4i000000000000-22−2i2i0000000000-22-22−2i2i−2i2i000000000000000000000000000000
χ694-44-44i−4i4i−4i00-2002-22−2i2i−2i2i000000−2i32i323−23002-22i−2i0000000000−1+31−3−1−31+3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000000000
χ704-44-44i−4i4i−4i00-2002-22−2i2i−2i2i000000−2i32i323−2300-22−2i2i00000000001−3−1+31+3−1−3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000000000
χ714-44-44i−4i4i−4i00-2002-22−2i2i−2i2i0000002i3−2i3−2323002-22i−2i0000000000−1−31+3−1+31−3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000000000
χ724-44-44i−4i4i−4i00-2002-22−2i2i−2i2i0000002i3−2i3−232300-22−2i2i00000000001+3−1−31−3−1+3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000000000
χ734-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i0000000000002-2−2i2i00000000002-22-2−2i2i−2i2i000000000000000000000000000000
χ744-44-4−4i4i−4i4i00400-44-4−4i4i−4i4i000000000000-222i−2i0000000000-22-222i−2i2i−2i000000000000000000000000000000
χ754-44-4−4i4i−4i4i00-2002-222i−2i2i−2i000000−2i32i3−2323002-2−2i2i0000000000−1−31+3−1+31−3ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11000000000000000000000000000000
χ764-44-4−4i4i−4i4i00-2002-222i−2i2i−2i000000−2i32i3−232300-222i−2i00000000001+3−1−31−3−1+3−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11000000000000000000000000000000
χ774-44-4−4i4i−4i4i00-2002-222i−2i2i−2i0000002i3−2i323−23002-2−2i2i0000000000−1+31−3−1−31+3−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11000000000000000000000000000000
χ784-44-4−4i4i−4i4i00-2002-222i−2i2i−2i0000002i3−2i323−2300-222i−2i00000000001−3−1+31+3−1−3ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11000000000000000000000000000000
χ794-4-444-4-4400400-4-444-4-44000000000000000000000000000000000000000000000000002-2002-200000000
χ804-4-444-4-4400400-4-444-4-4400000000000000000000000000000000000000000000000000-2200-2200000000
χ814-4-44-444-400400-4-44-444-4000000000000000000000000000000000000000000000000002-200-2200000000
χ824-4-44-444-400400-4-44-444-400000000000000000000000000000000000000000000000000-22002-200000000
χ838-8-888-8-8800-40044-4-444-40000000000000000000000000000000000000000000000000000000000000000
χ848-8-88-888-800-40044-44-4-440000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.