Finite Group Databasebeta

← Group #10690001

Character table — Group #10690001

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444444444444444444444448888121212121212121216161616161616161616242424242424242424242424
order122222223444444446666666448888888812121212121212121212121224242424242424242424242424242424444422224444441212121212121212444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1
χ91-1-111-11-111-1-111-11-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i11-1-1ii−i−i1-1ii−i−i11-1-1i−i1-1ii−i−i11-1-1
χ101-1-111-11-111-1-111-11-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i-1-111−i−iii1-1ii−i−i11-1-1−ii-11−i−iii-1-111
χ111-1-111-11-111-1-111-11-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii11-1-1−i−iii-11−i−iii-1-111−ii1-1ii−i−i-1-111
χ121-1-111-11-111-1-111-11-1-1-1-111-111-1iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-1-111ii−i−i-11−i−iii-1-111i−i-11−i−iii11-1-1
χ131-1-111-11-111-1-111-11-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i11-1-1ii−i−i-11ii−i−i-1-111i−i1-1−i−iii-1-111
χ141-1-111-11-111-1-111-11-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-1-111−i−iii-11ii−i−i-1-111−ii-11ii−i−i11-1-1
χ151-1-111-11-111-1-111-11-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii11-1-1−i−iii1-1−i−iii11-1-1−ii1-1−i−iii11-1-1
χ161-1-111-11-111-1-111-11-1-1-1-111-111-1−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii-1-111ii−i−i1-1−i−iii11-1-1i−i-11ii−i−i-1-111
χ17222222222222-2-2-22-22222222-2-200000000-2-2-2-2-2-22222-2-20000000000000000000022220000000000000000-2-200000000
χ18222222222222-2-2-22-22222222-2-200000000-2-2-2-2-2-22222-2-200000000000000000000-2-2-2-200000000000000002200000000
χ19222222222-2-2-2222-222222222-2-20000000022-2-222-2-2-2-2-2-200000000000000000000000022220000000000-2-20000000000
χ20222222222-2-2-2222-222222222-2-20000000022-2-222-2-2-2-2-2-2000000000000000000000000-2-2-2-20000000000220000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-2-2-2-2-22200000000000000002-22-200000000002-22-20000000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-222-2-2-2-2-2-2220000000000000000-22-220000000000-22-220000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122220000000022-1-1-1-1-1-1-1-1000000000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211111111000000000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111222200000000-2-2-1-1-1-11111000000000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2-2-200000000221111-1-1-1-1000000000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011-1-1111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i32-22-20000000000-11-11−i3i3−i3i3000000000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011-1-1111111-1-1−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-2200000000001-11-1i3−i3i3−i3000000000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011-1-1111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000000000-11-11i3−i3i3−i3000000000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011-1-1111111-1-1i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-2200000000001-11-1−i3i3−i3i3000000000000
χ31222-22-2-2-22-22-20002022-2-2-2-2200−i2−i2i2i2−i2−i2i2i20000002-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200002-22-2000000000000000000−i2i2−i2i20000
χ32222-22-2-2-22-22-20002022-2-2-2-2200−i2−i2i2i2−i2−i2i2i20000002-22-200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000-22-22000000000000000000i2−i2i2−i20000
χ33222-22-2-2-22-22-20002022-2-2-2-2200i2i2−i2−i2i2i2−i2−i20000002-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200002-22-2000000000000000000i2−i2i2−i20000
χ34222-22-2-2-22-22-20002022-2-2-2-2200i2i2−i2−i2i2i2−i2−i20000002-22-200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000-22-22000000000000000000−i2i2−i2i20000
χ3522-2-2-222-220002-2-2022-222-2-2-2002−22−22−22−22-2002-20000002−22−22−22−22−22−22−22−2000000002i−2i2i−2i000000000000000000−i2i2−i2i2
χ3622-2-2-222-220002-2-2022-222-2-2-2002−22−22−22−22-2002-20000002−22−22−22−22−22−22−22−200000000−2i2i−2i2i000000000000000000i2−i2i2−i2
χ3722-2-2-222-220002-2-2022-222-2-2-200−22−22−22−222-2002-2000000−22−22−22−22−22−22−22−22000000002i−2i2i−2i000000000000000000i2−i2i2−i2
χ3822-2-2-222-220002-2-2022-222-2-2-200−22−22−22−222-2002-2000000−22−22−22−22−22−22−22−2200000000−2i2i−2i2i000000000000000000−i2i2−i2i2
χ392-22-2-2-22220002-220-2-22-22-22-200−i2i2−i2i2i2−i2i2−i22-200-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000002-2-22000000000000000000−i2i2i2−i2
χ402-22-2-2-22220002-220-2-22-22-22-200−i2i2−i2i2i2−i2i2−i22-200-22000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000-222-2000000000000000000i2−i2−i2i2
χ412-22-2-2-22220002-220-2-22-22-22-200i2−i2i2−i2−i2i2−i2i22-200-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000002-2-22000000000000000000i2−i2−i2i2
χ422-22-2-2-22220002-220-2-22-22-22-200i2−i2i2−i2−i2i2−i2i22-200-22000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000-222-2000000000000000000−i2i2i2−i2
χ432-2-222-22-222-2-2-2-2222-2-2-222-22-2200000000-2-2-2-22222-2-2220000000000000000000022-2-20000000000000000-2200000000
χ442-2-222-22-222-2-2-2-2222-2-2-222-22-2200000000-2-2-2-22222-2-22200000000000000000000-2-22200000000000000002-200000000
χ452-2-222-22-22-22222-2-2-2-2-2-222-22-220000000022-2-2-2-2-2-222220000000000000000000000002i2i−2i−2i0000000000−2i2i0000000000
χ462-2-222-22-22-22222-2-2-2-2-2-222-22-220000000022-2-2-2-2-2-22222000000000000000000000000−2i−2i2i2i00000000002i−2i0000000000
χ472-2-222-22-22-222-2-22-22-2-2-222-222-200000000-2-22222-2-222-2-200000000000000002i−2i−2i2i00000000002i−2i−2i2i0000000000000000
χ482-2-222-22-22-222-2-22-22-2-2-222-222-200000000-2-22222-2-222-2-20000000000000000−2i2i2i−2i0000000000−2i2i2i−2i0000000000000000
χ492-2-222-22-2-12-2-222-22-2111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii2i2i−2i−2i000000002-2−i−iii-1-111000000000000
χ502-2-222-22-2-12-2-222-22-2111-1-11-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii−2i−2i2i2i00000000-22ii−i−i11-1-1000000000000
χ512-2-222-22-2-12-2-222-22-2111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i2i2i−2i−2i00000000-22−i−iii11-1-1000000000000
χ522-2-222-22-2-12-2-222-22-2111-1-11-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i−2i−2i2i2i000000002-2ii−i−i-1-111000000000000
χ532-2-222-22-2-1-222-2-22-22111-1-11-12-20000000011-1-1-1-111-1-1113333−3−3−3−3−3−3−3−333332i−2i−2i2i0000000000−iii−i−i3i3i3−i3000000000000
χ542-2-222-22-2-1-222-2-22-22111-1-11-12-20000000011-1-1-1-111-1-1113333−3−3−3−3−3−3−3−33333−2i2i2i−2i0000000000i−i−iii3−i3−i3i3000000000000
χ552-2-222-22-2-1-222-2-22-22111-1-11-12-20000000011-1-1-1-111-1-111−3−3−3−333333333−3−3−3−32i−2i−2i2i0000000000−iii−ii3−i3−i3i3000000000000
χ562-2-222-22-2-1-222-2-22-22111-1-11-12-20000000011-1-1-1-111-1-111−3−3−3−333333333−3−3−3−3−2i2i2i−2i0000000000i−i−ii−i3i3i3−i3000000000000
χ572-2-2-222-222-2-2200020-2-22-2-2220022−2−2−2−2220000002-2-220022−2−222−2−2−2−222−2−22200002-2-220000000000000000002−2−220000
χ582-2-2-222-222-2-2200020-2-22-2-2220022−2−2−2−2220000002-2-220022−2−222−2−2−2−222−2−2220000-222-2000000000000000000−222−20000
χ592-2-2-222-222-2-2200020-2-22-2-22200−2−22222−2−20000002-2-2200−2−222−2−22222−2−222−2−200002-2-22000000000000000000−222−20000
χ602-2-2-222-222-2-2200020-2-22-2-22200−2−22222−2−20000002-2-2200−2−222−2−22222−2−222−2−20000-222-20000000000000000002−2−220000
χ6144444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000222222-2-2-2-22200000000000000000000000000000000000000000000000000
χ6244444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-400000000-2-222-2-222222200000000000000000000000000000000000000000000000000
χ63444-44-4-4-444-44000-4044-4-4-4-440000000000000000-44-440000000000000000000000000000000000000000000000000000
χ64444-44-4-4-4-24-44000-40-2-22222-200000000000000002-22-20066−6−6−6−66666−6−6−6−6660000000000000000000000000000000000
χ65444-44-4-4-4-24-44000-40-2-22222-200000000000000002-22-200−6−66666−6−6−6−66666−6−60000000000000000000000000000000000
χ66444-44-4-4-4-2-44-400040-2-22222-200−2i2−2i22i22i2−2i2−2i22i22i2000000-22-2200i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i20000000000000000000000000000000000
χ67444-44-4-4-4-2-44-400040-2-22222-2002i22i2−2i2−2i22i22i2−2i2−2i2000000-22-2200−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i20000000000000000000000000000000000
χ6844-44-4-4-444000000004-4-4-444-4002i−2i−2i2i2i−2i−2i2i0000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000
χ6944-44-4-4-444000000004-4-4-444-400−2i2i2i−2i−2i2i2i−2i000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000
χ7044-44-4-4-44-200000000-2222-2-22002i−2i−2i2i2i−2i−2i2i00−2i32i3000000−2i32i32ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ220000000000000000000000000000000000
χ7144-44-4-4-44-200000000-2222-2-22002i−2i−2i2i2i−2i−2i2i002i3−2i30000002i3−2i32ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ142ζ22−2ζ22−2ζ222ζ222ζ14−2ζ14−2ζ142ζ140000000000000000000000000000000000
χ7244-44-4-4-44-200000000-2222-2-2200−2i2i2i−2i−2i2i2i−2i00−2i32i3000000−2i32i3−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ220000000000000000000000000000000000
χ7344-44-4-4-44-200000000-2222-2-2200−2i2i2i−2i−2i2i2i−2i002i3−2i30000002i3−2i3−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ14−2ζ222ζ222ζ22−2ζ22−2ζ142ζ142ζ14−2ζ140000000000000000000000000000000000
χ7444-4-4-444-44000-4440-44-444-4-4-40000000000-4400-4400000000000000000000000000000000000000000000000000000000
χ7544-4-4-444-4-20004-4-404-22-2-22220022−2222−2222−2222−22-2200-22000000−22−22−22−22−22−22−22−220000000000000000000000000000000000
χ7644-4-4-444-4-20004-4-404-22-2-222200−2222−2222−2222−2222-2200-220000002−22−22−22−22−22−22−22−20000000000000000000000000000000000
χ7744-4-4-444-4-2000-4440-4-22-2-222200000000002-2002-2000000i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000000000
χ7844-4-4-444-4-2000-4440-4-22-2-222200000000002-2002-2000000−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000000000
χ794-444-44-4-4400000000-444-44-4-4002-2-22-222-20000000000002-2-222-2-22-222-2-222-20000000000000000000000000000000000
χ804-444-44-4-4400000000-444-44-4-400-222-22-2-22000000000000-222-2-222-22-2-222-2-220000000000000000000000000000000000
χ814-444-44-4-4-2000000002-2-22-222002-2-22-222-200−2i32i30000002i3−2i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i30000000000000000000000000000000000
χ824-444-44-4-4-2000000002-2-22-222002-2-22-222-2002i3−2i3000000−2i32i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i30000000000000000000000000000000000
χ834-444-44-4-4-2000000002-2-22-22200-222-22-2-2200−2i32i30000002i3−2i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i30000000000000000000000000000000000
χ844-444-44-4-4-2000000002-2-22-22200-222-22-2-22002i3−2i3000000−2i32i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i30000000000000000000000000000000000
χ854-44-4-4-4444000-44-404-44-44-44-40000000000-44004-400000000000000000000000000000000000000000000000000000000
χ864-44-4-4-444-20004-440-42-22-22-2200−2i22i2−2i22i22i2−2i22i2−2i2-22002-2000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i20000000000000000000000000000000000
χ874-44-4-4-444-20004-440-42-22-22-22002i2−2i22i2−2i2−2i22i2−2i22i2-22002-2000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i20000000000000000000000000000000000
χ884-44-4-4-444-2000-44-4042-22-22-2200000000002-200-220000006−66−6−66−66−66−666−66−60000000000000000000000000000000000
χ894-44-4-4-444-2000-44-4042-22-22-2200000000002-200-22000000−66−666−66−66−66−6−66−660000000000000000000000000000000000
χ904-4-444-44-4-24-4-4-4-4444222-2-22-2-44000000002222-2-2-2-222-2-200000000000000000000000000000000000000000000000000
χ914-4-444-44-4-2-44444-4-4-4222-2-22-2-4400000000-2-2222222-2-2-2-200000000000000000000000000000000000000000000000000
χ924-4-4-444-44444-4000-40-4-44-4-4440000000000000000-444-40000000000000000000000000000000000000000000000000000
χ934-4-4-444-44-244-4000-4022-222-2-200000000000000002-2-2200i6i6−i6−i6−i6−i6i6i6−i6−i6i6i6i6i6−i6−i60000000000000000000000000000000000
χ944-4-4-444-44-244-4000-4022-222-2-200000000000000002-2-2200−i6−i6i6i6i6i6−i6−i6i6i6−i6−i6−i6−i6i6i60000000000000000000000000000000000
χ954-4-4-444-44-2-4-440004022-222-2-2002222−22−22−22−222222000000-222-200−2−222−2−22222−2−222−2−20000000000000000000000000000000000
χ964-4-4-444-44-2-4-440004022-222-2-200−22−2222222222−22−22000000-222-20022−2−222−2−2−2−222−2−2220000000000000000000000000000000000

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