Finite Group Databasebeta

← Group #10694439

Character table — Group #10694439

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222344444444666666644888888881212121212121212888888888888121224242424242424242424242424242424444444448888226666888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1
χ91-1-111-1-11111-1-1-111-1-1-1-1-11111-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11-111-1-1ii−i−i1-1
χ101-1-111-1-11111-1-1-111-1-1-1-1-11111-1iiii−i−i−i−i1111-1-1-1-11111-1-1-1-1−i−iii1-1iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11-1-111−i−iii-11
χ111-1-111-1-11111-1-1-111-1-1-1-1-11111-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1111-111-1-1−i−iii-11
χ121-1-111-1-11111-1-1-111-1-1-1-1-11111-1iiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-11-1-111ii−i−i1-1
χ131-1-111-1-11111-1-1-111-1-1-1-1-11111-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1ii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii11-1-1-11-1-111ii−i−i-11
χ141-1-111-1-11111-1-1-111-1-1-1-1-11111-1−i−i−i−iiiii1111-1-1-1-11111-1-1-1-1−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11-111-1-1−i−iii1-1
χ151-1-111-1-11111-1-1-111-1-1-1-1-11111-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-11-1-111−i−iii1-1
χ161-1-111-1-11111-1-1-111-1-1-1-1-11111-1−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-1-1111-111-1-1ii−i−i-11
χ1722222222222-22-2-2-222222222-2-20000000022-2-22-22-2000000000000-2-2000000000000000022-2-222-2-20000000000000000
χ1822222222222-22-2-2-222222222-2-20000000022-2-22-22-2000000000000-2-20000000000000000-2-222-2-2220000000000000000
χ19222222222-2-22-2222-22222222-2-200000000-2-222-22-22222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ20222222222-2-22-2222-22222222-2-200000000-2-222-22-22-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
χ21222222222-2-2-2-2-2-2-2-22222222222i2i−2i−2i2i2i−2i−2i-2-2-2-2-2-2-2-2000000000000222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ22222222222-2-2-2-2-2-2-2-2222222222−2i−2i2i2i−2i−2i2i2i-2-2-2-2-2-2-2-200000000000022−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i11111111000000000000-1-1−i−iii−i−iii33−3−333−3−300000000000000−i3i3−i3i3000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i−2i−2i2i2i−2i−2i11111111000000000000-1-1−i−iii−i−iii−3−333−3−33300000000000000i3−i3i3−i3000000
χ2922222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i11111111000000000000-1-1ii−i−iii−i−i33−3−333−3−300000000000000i3−i3i3−i3000000
χ3022222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i2i2i−2i−2i2i2i11111111000000000000-1-1ii−i−iii−i−i−3−333−3−33300000000000000−i3i3−i3i3000000
χ312222-2-2-2-2200-2022-2022-2-22-2-20000000000002-20-2022i2i−2i−2i2i2i−2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ322222-2-2-2-2200-2022-2022-2-22-2-20000000000002-20-2022i2i−2i−2i2i2i−2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ332222-2-2-2-2200-2022-2022-2-22-2-20000000000002-20-202−2i−2i2i2i−2i−2i2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ342222-2-2-2-2200-2022-2022-2-22-2-20000000000002-20-202−2i−2i2i2i−2i−2i2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ3522-2-222-2-222-202000-22-22-2-22-2002−22−22−22−22-200-2020−i2i2−i2i2−i2i2−i2i20000002−22−22−22−200000000002i−2i002i−2i−i2i2−i2i2000000000000
χ3622-2-222-2-222-202000-22-22-2-22-2002−22−22−22−22-200-2020i2−i2i2−i2i2−i2i2−i20000002−22−22−22−20000000000−2i2i00−2i2ii2−i2i2−i2000000000000
χ3722-2-222-2-222-202000-22-22-2-22-200−22−22−22−222-200-2020−i2i2−i2i2−i2i2−i2i2000000−22−22−22−220000000000−2i2i00−2i2i−i2i2−i2i2000000000000
χ3822-2-222-2-222-202000-22-22-2-22-200−22−22−22−222-200-2020i2−i2i2−i2i2−i2i2−i2000000−22−22−22−2200000000002i−2i002i−2ii2−i2i2−i2000000000000
χ3922-2-222-2-22-220-200022-22-2-22-200−i2i2i2−i2−i2i2i2−i2-220020-20−i2i2−i2i2−i2i2−i2i2000000−i2i2i2−i2−i2i2i2−i2000000002-2002-200i2−i2i2−i2000000000000
χ4022-2-222-2-22-220-200022-22-2-22-200−i2i2i2−i2−i2i2i2−i2-220020-20i2−i2i2−i2i2−i2i2−i2000000−i2i2i2−i2−i2i2i2−i200000000-2200-2200−i2i2−i2i2000000000000
χ4122-2-222-2-22-220-200022-22-2-22-200i2−i2−i2i2i2−i2−i2i2-220020-20−i2i2−i2i2−i2i2−i2i2000000i2−i2−i2i2i2−i2−i2i200000000-2200-2200i2−i2i2−i2000000000000
χ4222-2-222-2-22-220-200022-22-2-22-200i2−i2−i2i2i2−i2−i2i2-220020-20i2−i2i2−i2i2−i2i2−i2000000i2−i2−i2i2i2−i2−i2i2000000002-2002-200−i2i2−i2i2000000000000
χ432-22-22-22-222-20-20002-22-22-22-200−i2i2−i2i2i2−i2i2−i22-20020-20−i2i2−i2i2i2−i2i2−i2000000−i2i2−i2i2i2−i2i2−i200000000002-200-22−i2i2i2−i2000000000000
χ442-22-22-22-222-20-20002-22-22-22-200−i2i2−i2i2i2−i2i2−i22-20020-20i2−i2i2−i2−i2i2−i2i2000000−i2i2−i2i2i2−i2i2−i20000000000-22002-2i2−i2−i2i2000000000000
χ452-22-22-22-222-20-20002-22-22-22-200i2−i2i2−i2−i2i2−i2i22-20020-20−i2i2−i2i2i2−i2i2−i2000000i2−i2i2−i2−i2i2−i2i20000000000-22002-2−i2i2i2−i2000000000000
χ462-22-22-22-222-20-20002-22-22-22-200i2−i2i2−i2−i2i2−i2i22-20020-20i2−i2i2−i2−i2i2−i2i2000000i2−i2i2−i2−i2i2−i2i200000000002-200-22i2−i2−i2i2000000000000
χ472-22-22-22-22-2202000-2-22-22-22-2002−2−22−222−2-2200-2020−i2i2−i2i2i2−i2i2−i20000002−2−22−222−2000000002i−2i00−2i2i00i2−i2−i2i2000000000000
χ482-22-22-22-22-2202000-2-22-22-22-2002−2−22−222−2-2200-2020i2−i2i2−i2−i2i2−i2i20000002−2−22−222−200000000−2i2i002i−2i00−i2i2i2−i2000000000000
χ492-22-22-22-22-2202000-2-22-22-22-200−222−22−2−22-2200-2020−i2i2−i2i2i2−i2i2−i2000000−222−22−2−2200000000−2i2i002i−2i00i2−i2−i2i2000000000000
χ502-22-22-22-22-2202000-2-22-22-22-200−222−22−2−22-2200-2020i2−i2i2−i2−i2i2−i2i2000000−222−22−2−22000000002i−2i00−2i2i00−i2i2i2−i2000000000000
χ512-2-222-2-222222-22-2-2-2-2-2-2-2222-220000000022-2-2-22-22000000000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ522-2-222-2-222222-22-2-2-2-2-2-2-2222-220000000022-2-2-22-22000000000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ532-2-222-2-222-2-2222-2-22-2-2-2-22222-222-2-2-2-222-2-2-2-222220000000000002-222-2-2-2-22200000000000000000000000000000000
χ542-2-222-2-222-2-2222-2-22-2-2-2-22222-2-2-22222-2-2-2-2-2-222220000000000002-2-2-22222-2-200000000000000000000000000000000
χ552-2-222-2-222-2-2-22-2222-2-2-2-2222-2200000000-2-2222-22-22222-2-2-2-20000-22000000000000000000000000-2-222000000000000
χ562-2-222-2-222-2-2-22-2222-2-2-2-2222-2200000000-2-2222-22-2-2-2-2-222220000-2200000000000000000000000022-2-2000000000000
χ572-2-222-2-22-122-2-2-222-21111-1-1-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-11111000000002i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ582-2-222-2-22-122-2-2-222-21111-1-1-12-22i2i2i2i−2i−2i−2i−2i-1-1-1-1111100000000−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ592-2-222-2-22-122-2-2-222-21111-1-1-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-11111000000002i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ602-2-222-2-22-122-2-2-222-21111-1-1-12-2−2i−2i−2i−2i2i2i2i2i-1-1-1-1111100000000−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ612-2-222-2-22-1-2-2222-2-221111-1-1-12-222-2-2-2-2221111-1-1-1-1000000000000-11-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ622-2-222-2-22-1-2-2222-2-221111-1-1-12-222-2-2-2-2221111-1-1-1-1000000000000-11-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ632-2-222-2-22-1-2-2222-2-221111-1-1-12-2-2-22222-2-21111-1-1-1-1000000000000-1111-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ642-2-222-2-22-1-2-2222-2-221111-1-1-12-2-2-22222-2-21111-1-1-1-1000000000000-1111-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ652-2-22-222-220020-22-20-2-2222-2-20000000000002-2020-22i2i−2i−2i−2i−2i2i2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ662-2-22-222-220020-22-20-2-2222-2-20000000000002-2020-22i2i−2i−2i−2i−2i2i2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ672-2-22-222-220020-22-20-2-2222-2-20000000000002-2020-2−2i−2i2i2i2i2i−2i−2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ682-2-22-222-220020-22-20-2-2222-2-20000000000002-2020-2−2i−2i2i2i2i2i−2i−2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ6944444444-244-44-4-4-44-2-2-2-2-2-2-2-4-400000000-2-222-22-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-44-4444-4-2-2-2-2-2-2-2-4-40000000022-2-22-22-2000000000000220000000000000000000000000000000000000000
χ714444-4-4-4-440040-4-44044-4-44-4-4000000000000-44040-4000000000000000000000000000000000000000000000000000000
χ724444-4-4-4-4-20040-4-440-2-222-2220000000000002-20-20200000000000000000000006−6−666−6−66000000000000000000000000
χ734444-4-4-4-4-20040-4-440-2-222-2220000000000002-20-2020000000000000000000000−666−6−666−6000000000000000000000000
χ744444-4-4-4-4-200-4044-40-2-222-222000000000000-22020-20000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ754444-4-4-4-4-200-4044-40-2-222-222000000000000-22020-200000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7644-4-444-4-4-24-404000-4-22-222-220022−2222−2222−2222−22-220020-2000000000000000−22−22−22−2200000000000000000000000000000000
χ7744-4-444-4-4-24-404000-4-22-222-2200−2222−2222−2222−2222-220020-20000000000000002−22−22−22−200000000000000000000000000000000
χ7844-4-444-4-4-2-440-40004-22-222-2200−2i22i22i2−2i2−2i22i22i2−2i22-200-202000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ7944-4-444-4-4-2-440-40004-22-222-22002i2−2i2−2i22i22i2−2i2−2i22i22-200-202000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ8044-4-4-4-4444000000004-4-44-4-4400000000000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ8144-4-4-4-4444000000004-4-44-4-44000000000000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ824-44-44-44-4-24-40-400042-22-22-2200−2i22i2−2i22i22i2−2i22i2−2i2-2200-202000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ834-44-44-44-4-24-40-400042-22-22-22002i2−2i22i2−2i2−2i22i2−2i22i2-2200-202000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ844-44-44-44-4-2-4404000-42-22-22-220022−22−2222−222222−222-20020-2000000000000000−222−22−2−2200000000000000000000000000000000
χ854-44-44-44-4-2-4404000-42-22-22-2200−222222−2222−22−22222-20020-20000000000000002−2−22−222−200000000000000000000000000000000
χ864-44-4-44-44400000000-444-4-4-4400000000000000000022−22−2222−222222−220000000000000000000000000000000000000000000000
χ874-44-4-44-44400000000-444-4-4-44000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000000000
χ884-4-444-4-44-2444-44-4-4-42222-2-2-2-4400000000-2-2222-22-20000000000002-20000000000000000000000000000000000000000
χ894-4-444-4-44-2-4-4-44-44442222-2-2-2-440000000022-2-2-22-220000000000002-20000000000000000000000000000000000000000
χ904-4-44-444-4400-404-440-4-4444-4-4000000000000-440-404000000000000000000000000000000000000000000000000000000
χ914-4-44-444-4-20040-44-4022-2-2-222000000000000-220-20200000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ924-4-44-444-4-20040-44-4022-2-2-222000000000000-220-202000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ934-4-44-444-4-200-404-44022-2-2-2220000000000002-2020-20000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ944-4-44-444-4-200-404-44022-2-2-2220000000000002-2020-20000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ9588-8-8-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-88-88-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000

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