Finite Group Databasebeta

← Group #10693848

Character table — Group #10693848

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666448888888812121212121212128888888888881212242424242424242424242424242424244444444488884412121212888844
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
χ91-1111-1-1-111-1-1-1-1111-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-11111-1-1-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i11-1-1i−iii−i−i11-1-1i−i
χ101-1111-1-1-111-1-1-1-1111-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-11111-1-1-1-1-1-1111-1iiii−i−i−i−i-1-1-1-11111ii−i−iii−i−i11-1-1−ii−i−iii-1-111−ii
χ111-1111-1-1-111-1-1-1-1111-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1-1-1-1-1111111-1-11-1iiii−i−i−i−i1111-1-1-1-1−i−iii−i−iii-1-111i−iii−i−i-1-111−ii
χ121-1111-1-1-111-1-1-1-1111-1-1-1111-11-1iiii−i−i−i−i111-1-1-11-1-1-1-1-11111-1-1111-1iiii−i−i−i−i-1-1-1-11111−i−iii−i−iii-1-111−ii−i−iii11-1-1i−i
χ131-1111-1-1-111-1-1-1-1111-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-11111-1-1-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii11-1-1−ii−i−iii11-1-1−ii
χ141-1111-1-1-111-1-1-1-1111-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-11111-1-1-1-1-1-1111-1−i−i−i−iiiii-1-1-1-11111−i−iii−i−iii11-1-1i−iii−i−i-1-111i−i
χ151-1111-1-1-111-1-1-1-1111-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1-1-1-1-1111111-1-11-1−i−i−i−iiiii1111-1-1-1-1ii−i−iii−i−i-1-111−ii−i−iii-1-111i−i
χ161-1111-1-1-111-1-1-1-1111-1-1-1111-11-1−i−i−i−iiiii111-1-1-11-1-1-1-1-11111-1-1111-1−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i-1-111i−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-222222222-2-2000000002-2-222-22-2000000000000-2-200000000000000002222-2-2-2-20000000000000000
χ18222222222222-2-2-2-222222222-2-2000000002-2-222-22-2000000000000-2-20000000000000000-2-2-2-222220000000000000000
χ19222222222-2-2-22222-22222222-2-200000000-222-2-22-22222222220000-2-2000000000000000000000000-2-2-2-2000000000000
χ20222222222-2-2-22222-22222222-2-200000000-222-2-22-22-2-2-2-2-2-2-2-20000-2-20000000000000000000000002222000000000000
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
χ31222-2-22-2-22000-222-202-2-22-2-22000000000002-200-2022i2i−2i−2i2i2i−2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ32222-2-22-2-22000-222-202-2-22-2-22000000000002-200-2022i2i−2i−2i2i2i−2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ33222-2-22-2-22000-222-202-2-22-2-22000000000002-200-202−2i−2i2i2i−2i−2i2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ34222-2-22-2-22000-222-202-2-22-2-22000000000002-200-202−2i−2i2i2i−2i−2i2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ3522-22-2-22-2222-20000-222-2-22-2-2002−22−22−22−22002-20-202−22−22−22−20000002−22−22−22−2000000002-22-200002−22−2000000000000
χ3622-22-2-22-2222-20000-222-2-22-2-2002−22−22−22−22002-20-20−22−22−22−220000002−22−22−22−200000000-22-220000−22−22000000000000
χ3722-22-2-22-2222-20000-222-2-22-2-200−22−22−22−222002-20-202−22−22−22−2000000−22−22−22−2200000000-22-2200002−22−2000000000000
χ3822-22-2-22-2222-20000-222-2-22-2-200−22−22−22−222002-20-20−22−22−22−22000000−22−22−22−22000000002-22-20000−22−22000000000000
χ3922-22-2-22-22-2-220000222-2-22-2-200−i2i2i2−i2−i2i2i2−i2-200-220202−22−22−22−2000000−i2i2i2−i2−i2i2i2−i20000000000002i−2i2i−2i−22−22000000000000
χ4022-22-2-22-22-2-220000222-2-22-2-200−i2i2i2−i2−i2i2i2−i2-200-22020−22−22−22−22000000−i2i2i2−i2−i2i2i2−i2000000000000−2i2i−2i2i2−22−2000000000000
χ4122-22-2-22-22-2-220000222-2-22-2-200i2−i2−i2i2i2−i2−i2i2-200-220202−22−22−22−2000000i2−i2−i2i2i2−i2−i2i2000000000000−2i2i−2i2i−22−22000000000000
χ4222-22-2-22-22-2-220000222-2-22-2-200i2−i2−i2i2i2−i2−i2i2-200-22020−22−22−22−22000000i2−i2−i2i2i2−i2−i2i20000000000002i−2i2i−2i2−22−2000000000000
χ432-2222-2-2-222-2-222-2-22-2-2-2222-2-22000000002-2-2-2-2222000000000000-2200000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ442-2222-2-2-222-2-222-2-22-2-2-2222-2-22000000002-2-2-2-2222000000000000-220000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ452-2222-2-2-22-22222-2-2-2-2-2-2222-22-222-2-2-2-222-2-2-2222-220000000000002-222-2-2-2-22200000000000000000000000000000000
χ462-2222-2-2-22-22222-2-2-2-2-2-2222-22-2-2-22222-2-2-2-2-2222-220000000000002-2-2-22222-2-200000000000000000000000000000000
χ472-2222-2-2-22-222-2-222-2-2-2-2222-2-2200000000-22222-2-2-22222-2-2-2-20000-22000000000000000000000000-2-222000000000000
χ482-2222-2-2-22-222-2-222-2-2-2-2222-2-2200000000-22222-2-2-2-2-2-2-222220000-2200000000000000000000000022-2-2000000000000
χ492-2222-2-2-2-12-2-2-2-2222111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1111-110000000022-2-2-11−i−i−i−iiiii-1-1-1-111110000000000002i−2i−i−iii000000
χ502-2222-2-2-2-12-2-2-2-2222111-1-1-112-22i2i2i2i−2i−2i−2i−2i-1-1-1111-1100000000-2-222-11−i−i−i−iiiii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ512-2222-2-2-2-12-2-2-2-2222111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1111-110000000022-2-2-11iiii−i−i−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ522-2222-2-2-2-12-2-2-2-2222111-1-1-112-2−2i−2i−2i−2i2i2i2i2i-1-1-1111-1100000000-2-222-11iiii−i−i−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ532-2222-2-2-2-1-22222-2-2-2111-1-1-112-222-2-2-2-222111-1-1-11-1000000000000-11-1-11111-1-133−3−3−3−33300000000000000−333−3000000
χ542-2222-2-2-2-1-22222-2-2-2111-1-1-112-222-2-2-2-222111-1-1-11-1000000000000-11-1-11111-1-1−3−33333−3−3000000000000003−3−33000000
χ552-2222-2-2-2-1-22222-2-2-2111-1-1-112-2-2-22222-2-2111-1-1-11-1000000000000-1111-1-1-1-11133−3−3−3−333000000000000003−3−33000000
χ562-2222-2-2-2-1-22222-2-2-2111-1-1-112-2-2-22222-2-2111-1-1-11-1000000000000-1111-1-1-1-111−3−33333−3−300000000000000−333−3000000
χ572-22-2-2-22220002-22-20-2222-2-2-2000000000002-20020-22i2i−2i−2i−2i−2i2i2i2−2−2200000000002−22−2−22−22000000000000000000−i2i2i2−i200
χ582-22-2-2-22220002-22-20-2222-2-2-2000000000002-20020-22i2i−2i−2i−2i−2i2i2i−222−20000000000−22−222−22−2000000000000000000i2−i2−i2i200
χ592-22-2-2-22220002-22-20-2222-2-2-2000000000002-20020-2−2i−2i2i2i2i2i−2i−2i2−2−2200000000002−22−2−22−22000000000000000000i2−i2−i2i200
χ602-22-2-2-22220002-22-20-2222-2-2-2000000000002-20020-2−2i−2i2i2i2i2i−2i−2i−222−20000000000−22−222−22−2000000000000000000−i2i2i2−i200
χ612-2-22-22-2222-220000-2-2-22-22-2200−i2i2−i2i2i2−i2i2−i2200-220-202−22−2−22−22000000−i2i2−i2i2i2−i2i2−i200000000−2i2i2i−2i00002−2−22000000000000
χ622-2-22-22-2222-220000-2-2-22-22-2200−i2i2−i2i2i2−i2i2−i2200-220-20−22−222−22−2000000−i2i2−i2i2i2−i2i2−i2000000002i−2i−2i2i0000−222−2000000000000
χ632-2-22-22-2222-220000-2-2-22-22-2200i2−i2i2−i2−i2i2−i2i2200-220-202−22−2−22−22000000i2−i2i2−i2−i2i2−i2i2000000002i−2i−2i2i00002−2−22000000000000
χ642-2-22-22-2222-220000-2-2-22-22-2200i2−i2i2−i2−i2i2−i2i2200-220-20−22−222−22−2000000i2−i2i2−i2−i2i2−i2i200000000−2i2i2i−2i0000−222−2000000000000
χ652-2-22-22-222-22-200002-2-22-22-22002−2−22−222−2-2002-20202−22−2−22−220000002−2−22−222−2000000000000-222-2−222−2000000000000
χ662-2-22-22-222-22-200002-2-22-22-22002−2−22−222−2-2002-2020−22−222−22−20000002−2−22−222−20000000000002-2-222−2−22000000000000
χ672-2-22-22-222-22-200002-2-22-22-2200−222−22−2−22-2002-20202−22−2−22−22000000−222−22−2−220000000000002-2-22−222−2000000000000
χ682-2-22-22-222-22-200002-2-22-22-2200−222−22−2−22-2002-2020−22−222−22−2000000−222−22−2−22000000000000-222-22−2−22000000000000
χ6944444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-400000000-222-2-22-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-4000000002-2-222-22-2000000000000220000000000000000000000000000000000000000
χ71444-4-44-4-440004-4-4404-4-44-4-4400000000000-440040-4000000000000000000000000000000000000000000000000000000
χ72444-4-44-4-4-20004-4-440-222-222-2000000000002-200-20200000000000000000000006−6−666−6−66000000000000000000000000
χ73444-4-44-4-4-20004-4-440-222-222-2000000000002-200-2020000000000000000000000−666−6−666−6000000000000000000000000
χ74444-4-44-4-4-2000-444-40-222-222-200000000000-220020-20000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ75444-4-44-4-4-2000-444-40-222-222-200000000000-220020-200000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7644-44-4-44-4-244-40000-4-2-222-2220022−2222−2222−2222−22-200-2202000000000000000−22−22−22−2200000000000000000000000000000000
χ7744-44-4-44-4-244-40000-4-2-222-22200−2222−2222−2222−2222-200-22020000000000000002−22−22−22−200000000000000000000000000000000
χ7844-44-4-44-4-2-4-4400004-2-222-22200−2i22i22i2−2i2−2i22i22i2−2i22002-20-2000000000000000i2−i2−i2i2i2−i2−i2i200000000000000000000000000000000
χ7944-44-4-44-4-2-4-4400004-2-222-222002i2−2i2−2i22i22i2−2i2−2i22i22002-20-2000000000000000−i2i2i2−i2−i2i2i2−i200000000000000000000000000000000
χ8044-4-44-4-444000000004-44-4-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ8144-4-44-4-444000000004-44-4-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ824-4444-4-4-4-24-4-444-4-44222-2-2-22-4400000000-22222-2-2-20000000000002-20000000000000000000000000000000000000000
χ834-4444-4-4-4-2-444-4-444-4222-2-2-22-44000000002-2-2-2-22220000000000002-20000000000000000000000000000000000000000
χ844-44-4-4-4444000-44-440-4444-4-4-400000000000-4400-404000000000000000000000000000000000000000000000000000000
χ854-44-4-4-444-20004-44-402-2-2-222200000000000-2200-2020000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ864-44-4-4-444-20004-44-402-2-2-222200000000000-2200-20200000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ874-44-4-4-444-2000-44-4402-2-2-2222000000000002-20020-200000000000000000000006−6−66−666−6000000000000000000000000
χ884-44-4-4-444-2000-44-4402-2-2-2222000000000002-20020-20000000000000000000000−666−66−6−66000000000000000000000000
χ894-4-44-44-44-24-440000-422-22-22-200−2i22i2−2i22i22i2−2i22i2−2i2-2002-202000000000000000i2−i2i2−i2−i2i2−i2i200000000000000000000000000000000
χ904-4-44-44-44-24-440000-422-22-22-2002i2−2i22i2−2i2−2i22i2−2i22i2-2002-202000000000000000−i2i2−i2i2i2−i2i2−i200000000000000000000000000000000
χ914-4-44-44-44-2-44-40000422-22-22-20022−22−2222−222222−22200-220-2000000000000000−222−22−2−2200000000000000000000000000000000
χ924-4-44-44-44-2-44-40000422-22-22-200−222222−2222−22−2222200-220-20000000000000002−2−22−222−200000000000000000000000000000000
χ934-4-4-4444-4400000000-44-4-4-444000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ944-4-4-4444-4400000000-44-4-4-4440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ9588-8-88-8-88-400000000-44-444-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-4000000004-4444-4-4000000000000000000000000000000000000000000000000000000000000000000000000

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