Finite Group Databasebeta

← Group #10698229

Character table — Group #10698229

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111111122222222222222224444444444444444444444444444444444444416161616161616161616161624242424242424242424242424242424
order12222222344444444666666644888888881212121212121212121212122424242424242424242424242424242422446666121212124444444488888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ9222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-20000000000000000000000000000002200-2-200000000
χ10222222222222-2-2-22-22222222-2-2000000002222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2002200000000
χ11222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-200000000000000000000000000002200-2-20000000000
χ12222222222-2-2-2222-222222222-2-200000000-2-2-2-22222-2-2-2-20000000000000000000000000000-2-200220000000000
χ13222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-222220000000000000000002-2000022-2-20000000000000000
χ14222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-22222000000000000000000-220000-2-2220000000000000000
χ1522222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000000000
χ1622222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111110000000000000000
χ1722222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1111111111111111122-2-2-1-1-1-111110000000000000000
χ1822222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-2-2221111-1-1-1-10000000000000000
χ1922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i3002-2−i3−i3i3i3-1-1110000000000000000
χ2022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3i3i3i3i300-22i3i3−i3−i311-1-10000000000000000
χ2122222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3002-2i3i3−i3−i3-1-1110000000000000000
χ2222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1220000000011111111-1-1-1-1i3i3i3i3i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i300-22−i3−i3i3i311-1-10000000000000000
χ23222-2-22-2-220002-2-20222-22-2-2-200−i2−i2−i2−i2i2i2i2i2000022-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000002-2000000−i2−i2i2i20000
χ24222-2-22-2-220002-2-20222-22-2-2-200−i2−i2−i2−i2i2i2i2i2000022-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2000000000000-22000000i2i2−i2−i20000
χ25222-2-22-2-220002-2-20222-22-2-2-200i2i2i2i2−i2−i2−i2−i2000022-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000002-2000000i2i2−i2−i20000
χ26222-2-22-2-220002-2-20222-22-2-2-200i2i2i2i2−i2−i2−i2−i2000022-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2000000000000-22000000−i2−i2i2i20000
χ2722-22-2-22-2222-2000-202-2-2-22-220022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−20000000000000000002i−2i0000−i2−i2i2i2
χ2822-22-2-22-2222-2000-202-2-2-22-220022−2−222−2−222-2-20000000022−2−222−2−222−2−222−2−2000000000000000000−2i2i0000i2i2−i2−i2
χ2922-22-2-22-2222-2000-202-2-2-22-2200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−2220000000000000000002i−2i0000i2i2−i2−i2
χ3022-22-2-22-2222-2000-202-2-2-22-2200−2−222−2−22222-2-200000000−2−222−2−222−2−222−2−222000000000000000000−2i2i0000−i2−i2i2i2
χ312-2222-2-2-222-2222-2-2-2-2-2-2222-22-2000000002-22-22-22-222-2-200000000000000002-2002-22-200000000000000000000
χ322-2222-2-2-222-2222-2-2-2-2-2-2222-22-2000000002-22-22-22-222-2-20000000000000000-2200-22-2200000000000000000000
χ332-2222-2-2-222-22-2-22-22-2-2-2222-2-22000000002-22-2-22-22-2-2220000000000000000000000000000000000002i−2i2i−2i0000
χ342-2222-2-2-222-22-2-22-22-2-2-2222-2-22000000002-22-2-22-22-2-222000000000000000000000000000000000000−2i2i−2i2i0000
χ352-2222-2-2-22-22-222-22-2-2-2-2222-2-2200000000-22-222-22-2-2-22200000000000000000000000000000000000000002i−2i2i−2i
χ362-2222-2-2-22-22-222-22-2-2-2-2222-2-2200000000-22-222-22-2-2-2220000000000000000000000000000000000000000−2i2i−2i2i
χ372-2222-2-2-22-22-2-2-2222-2-2-2222-22-22i−2i2i−2i2i−2i2i−2i-22-22-22-2222-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000
χ382-2222-2-2-22-22-2-2-2222-2-2-2222-22-2−2i2i−2i2i−2i2i−2i2i-22-22-22-2222-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000
χ392-2222-2-2-2-12-2222-2-2-2111-1-1-112-200000000-11-11-11-11-1-1113−33−33−33−3−33−33−33−332-200-11-113−33−30000000000000000
χ402-2222-2-2-2-12-2222-2-2-2111-1-1-112-200000000-11-11-11-11-1-1113−33−33−33−3−33−33−33−33-22001-11-1−33−330000000000000000
χ412-2222-2-2-2-12-2222-2-2-2111-1-1-112-200000000-11-11-11-11-1-111−33−33−33−333−33−33−33−32-200-11-11−33−330000000000000000
χ422-2222-2-2-2-12-2222-2-2-2111-1-1-112-200000000-11-11-11-11-1-111−33−33−33−333−33−33−33−3-22001-11-13−33−30000000000000000
χ432-2222-2-2-2-1-22-2-2-2222111-1-1-112-22i−2i2i−2i2i−2i2i−2i1-11-11-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000−i3i3i3−i33−3−330000000000000000
χ442-2222-2-2-2-1-22-2-2-2222111-1-1-112-22i−2i2i−2i2i−2i2i−2i1-11-11-11-1-1-111−ii−ii−ii−ii−ii−ii−ii−ii0000i3−i3−i3i3−333−30000000000000000
χ452-2222-2-2-2-1-22-2-2-2222111-1-1-112-2−2i2i−2i2i−2i2i−2i2i1-11-11-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000−i3i3i3−i3−333−30000000000000000
χ462-2222-2-2-2-1-22-2-2-2222111-1-1-112-2−2i2i−2i2i−2i2i−2i2i1-11-11-11-1-1-111i−ii−ii−ii−ii−ii−ii−ii−i0000i3−i3−i3i33−3−330000000000000000
χ472-22-2-2-2222000-22-202-2-222-2-22002−22−2−22−220000-222-200002−22−2−22−222−22−2−22−2200000000000000002-2002−2−220000
χ482-22-2-2-2222000-22-202-2-222-2-22002−22−2−22−220000-222-200002−22−2−22−222−22−2−22−220000000000000000-2200−222−20000
χ492-22-2-2-2222000-22-202-2-222-2-2200−22−222−22−20000-222-20000−22−222−22−2−22−222−22−200000000000000002-200−222−20000
χ502-22-2-2-2222000-22-202-2-222-2-2200−22−222−22−20000-222-20000−22−222−22−2−22−222−22−20000000000000000-22002−2−220000
χ512-2-22-22-222-222000-20-222-22-2-200−i2i2i2−i2−i2i2i2−i2-222-200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000002i−2i000000002−2−22
χ522-2-22-22-222-222000-20-222-22-2-200−i2i2i2−i2−i2i2i2−i2-222-200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000000000−2i2i00000000−222−2
χ532-2-22-22-222-222000-20-222-22-2-200i2−i2−i2i2i2−i2−i2i2-222-200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000002i−2i00000000−222−2
χ542-2-22-22-222-222000-20-222-22-2-200i2−i2−i2i2i2−i2−i2i2-222-200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000000000−2i2i000000002−2−22
χ5544444444-2444-4-4-44-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222222200000000000000000000000000000000000000000000
χ5644444444-2-4-4-4444-44-2-2-2-2-2-2-2-4-4000000002222-2-2-2-2222200000000000000000000000000000000000000000000
χ57444-4-44-4-44000-4440-444-44-4-4-400000000000000-4-444000000000000000000000000000000000000000000000000
χ58444-4-44-4-4-20004-4-404-2-22-222200−2i2−2i2−2i2−2i22i22i22i22i20000-2-2220000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i20000000000000000000000000000
χ59444-4-44-4-4-20004-4-404-2-22-2222002i22i22i22i2−2i2−2i2−2i2−2i20000-2-2220000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i20000000000000000000000000000
χ60444-4-44-4-4-2000-4440-4-2-22-22220000000000000022-2-200006666−6−6−6−6−6−6−6−666660000000000000000000000000000
χ61444-4-44-4-4-2000-4440-4-2-22-22220000000000000022-2-20000−6−6−6−666666666−6−6−6−60000000000000000000000000000
χ6244-44-4-44-44-4-44000404-4-4-44-440000000000-4-4440000000000000000000000000000000000000000000000000000
χ6344-44-4-44-4-244-4000-40-2222-22-2002222−22−222222−22−22-2-22200000000−2−222−2−222−2−222−2−2220000000000000000000000000000
χ6444-44-4-44-4-244-4000-40-2222-22-200−22−222222−22−222222-2-2220000000022−2−222−2−222−2−222−2−20000000000000000000000000000
χ6544-44-4-44-4-2-4-4400040-2222-22-2000000000022-2-200000000i6i6−i6−i6i6i6−i6−i6−i6−i6i6i6−i6−i6i6i60000000000000000000000000000
χ6644-44-4-44-4-2-4-4400040-2222-22-2000000000022-2-200000000−i6−i6i6i6−i6−i6i6i6i6i6−i6−i6i6i6−i6−i60000000000000000000000000000
χ6744-4-44-4-444000000004-44-4-44-4002i2i−2i−2i−2i−2i2i2i0000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ6844-4-44-4-444000000004-44-4-44-400−2i−2i2i2i2i2i−2i−2i000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ6944-4-44-4-44-200000000-22-222-22002i2i−2i−2i−2i−2i2i2i00000000−2i32i3−2i32i32ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ142ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ220000000000000000000000000000
χ7044-4-44-4-44-200000000-22-222-22002i2i−2i−2i−2i−2i2i2i000000002i3−2i32i3−2i32ζ222ζ22−2ζ22−2ζ22−2ζ22−2ζ222ζ222ζ222ζ142ζ14−2ζ14−2ζ14−2ζ14−2ζ142ζ142ζ140000000000000000000000000000
χ7144-4-44-4-44-200000000-22-222-2200−2i−2i2i2i2i2i−2i−2i00000000−2i32i3−2i32i3−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ14−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ220000000000000000000000000000
χ7244-4-44-4-44-200000000-22-222-2200−2i−2i2i2i2i2i−2i−2i000000002i3−2i32i3−2i3−2ζ22−2ζ222ζ222ζ222ζ222ζ22−2ζ22−2ζ22−2ζ14−2ζ142ζ142ζ142ζ142ζ14−2ζ14−2ζ140000000000000000000000000000
χ734-4444-4-4-4-24-44-4-44-44222-2-2-22-4400000000-22-222-22-222-2-200000000000000000000000000000000000000000000
χ744-4444-4-4-4-2-44-444-44-4222-2-2-22-44000000002-22-2-22-2222-2-200000000000000000000000000000000000000000000
χ754-44-4-4-44440004-440-4-4-444-4-44000000000000004-4-44000000000000000000000000000000000000000000000000
χ764-44-4-4-444-20004-440-422-2-222-200000000000000-222-20000i6−i6i6−i6−i6i6−i6i6−i6i6−i6i6i6−i6i6−i60000000000000000000000000000
χ774-44-4-4-444-20004-440-422-2-222-200000000000000-222-20000−i6i6−i6i6i6−i6i6−i6i6−i6i6−i6−i6i6−i6i60000000000000000000000000000
χ784-44-4-4-444-2000-44-40422-2-222-20022−2222−22−2222−222200002-2-220000−22−222−22−2−22−222−22−20000000000000000000000000000
χ794-44-4-4-444-2000-44-40422-2-222-200−2222−222222−2222−2200002-2-2200002−22−2−22−222−22−2−22−220000000000000000000000000000
χ804-4-44-44-4444-4-400040-444-44-4-400000000004-4-440000000000000000000000000000000000000000000000000000
χ814-4-44-44-44-24-4-4000402-2-22-2220000000000-222-2000000006−6−666−6−66−666−6−666−60000000000000000000000000000
χ824-4-44-44-44-24-4-4000402-2-22-2220000000000-222-200000000−666−6−666−66−6−666−6−660000000000000000000000000000
χ834-4-44-44-44-2-444000-402-2-22-22200−2i22i22i2−2i2−2i22i22i2−2i22-2-2200000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i20000000000000000000000000000
χ844-4-44-44-44-2-444000-402-2-22-222002i2−2i2−2i22i22i2−2i2−2i22i22-2-2200000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i20000000000000000000000000000
χ854-4-4-4444-4400000000-44-4-4-444002-2-22-222-20000000000002-2-22-222-22-2-22-222-20000000000000000000000000000
χ864-4-4-4444-4400000000-44-4-4-44400-222-22-2-22000000000000-222-22-2-22-222-22-2-220000000000000000000000000000
χ874-4-4-4444-4-2000000002-2222-2-2002-2-22-222-200000000−2i32i32i3−2i3−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i30000000000000000000000000000
χ884-4-4-4444-4-2000000002-2222-2-2002-2-22-222-2000000002i3−2i3−2i32i3−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i30000000000000000000000000000
χ894-4-4-4444-4-2000000002-2222-2-200-222-22-2-2200000000−2i32i32i3−2i31−i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i30000000000000000000000000000
χ904-4-4-4444-4-2000000002-2222-2-200-222-22-2-22000000002i3−2i3−2i32i31+i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i30000000000000000000000000000

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