Finite Group Databasebeta

← Group #10690849

Character table — Group #10690849

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222344444444666666644888888881212121212121212222244448888121224242424242424242424242424242424444488888888226666888844
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
χ511111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ9111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11iiii−i−i−i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ10111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11iiii−i−i−i−i−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii-11
χ11111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11iiii−i−i−i−iiiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1−i−iii-11
χ12111111111-1-1-1-1-1-1-1-1111111111iiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11iiii−i−i−i−i−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i1-1
χ13111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11
χ14111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-11111-1-1-1-1−i−iii11−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1
χ15111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i11−i−i−i−iiiiiiiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii1-1
χ16111111111-1-1-1-1-1-1-1-1111111111−i−i−i−iiiii-1-1-1-1-1-1-1-1-1-1-1-11111−i−iii11−i−i−i−iiiii−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1ii−i−i-11
χ17222222222222-2-2-2-222222222-2-200000000222-2-2-22-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ18222222222222-2-2-2-222222222-2-200000000222-2-2-22-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-2-22222-22222222-2-200000000-2-2-2222-222222-2-2-2-20000-2-20000000000000000-2-22200000000000000000000
χ20222222222-2-2-22222-22222222-2-200000000-2-2-2222-22-2-2-2-222220000-2-2000000000000000022-2-200000000000000000000
χ2122222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2222222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000000000-2-21111000000
χ2322222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000002222-1-111111111-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2422222222-122222222-1-1-1-1-1-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000000-2-2-2-2-1-1111111111111111100000000000022-1-1-1-1000000
χ2522222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i11111111000000002i2i−2i−2i-1-1−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ2622222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1222i2i2i2i−2i−2i−2i−2i1111111100000000−2i−2i2i2i-1-1−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ2722222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i11111111000000002i2i−2i−2i-1-1iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ2822222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-122−2i−2i−2i−2i2i2i2i2i1111111100000000−2i−2i2i2i-1-1iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ29222-22-2-2-220002-22-2022-2-22-2-20022−2−222−2−20002-2-20200002i2i−2i−2i00000022−2−222−2−2000000002i−2i00−i2−i2i2i2−i2−i2i2i2000000000000
χ30222-22-2-2-220002-22-2022-2-22-2-20022−2−222−2−20002-2-2020000−2i−2i2i2i00000022−2−222−2−200000000−2i2i00i2i2−i2−i2i2i2−i2−i2000000000000
χ31222-22-2-2-220002-22-2022-2-22-2-200−2−222−2−2220002-2-20200002i2i−2i−2i000000−2−222−2−222000000002i−2i00i2i2−i2−i2i2i2−i2−i2000000000000
χ32222-22-2-2-220002-22-2022-2-22-2-200−2−222−2−2220002-2-2020000−2i−2i2i2i000000−2−222−2−22200000000−2i2i00−i2−i2i2i2−i2−i2i2i2000000000000
χ33222-22-2-2-22000-22-22022-2-22-2-200−i2−i2i2i2i2i2−i2−i2000-2220-200002i2i−2i−2i000000−i2−i2i2i2i2i2−i2−i200000000−2i2i0022−2−2−2−222000000000000
χ34222-22-2-2-22000-22-22022-2-22-2-200−i2−i2i2i2i2i2−i2−i2000-2220-20000−2i−2i2i2i000000−i2−i2i2i2i2i2−i2−i2000000002i−2i00−2−22222−2−2000000000000
χ35222-22-2-2-22000-22-22022-2-22-2-200i2i2−i2−i2−i2−i2i2i2000-2220-200002i2i−2i−2i000000i2i2−i2−i2−i2−i2i2i200000000−2i2i00−2−22222−2−2000000000000
χ36222-22-2-2-22000-22-22022-2-22-2-200i2i2−i2−i2−i2−i2i2i2000-2220-20000−2i−2i2i2i000000i2i2−i2−i2−i2−i2i2i2000000002i−2i0022−2−2−2−222000000000000
χ3722-2-2-22-22222-20000-22-22-2-22-2000000000022-2000-2022-2-22-22-2−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000−i2i2−i2i200
χ3822-2-2-22-22222-20000-22-22-2-22-2000000000022-2000-2022-2-22-22-2i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000i2−i2i2−i200
χ3922-2-2-22-22222-20000-22-22-2-22-2000000000022-2000-20-2-222-22-22−i2i2−i2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000i2−i2i2−i200
χ4022-2-2-22-22222-20000-22-22-2-22-2000000000022-2000-20-2-222-22-22i2−i2i2−i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000−i2i2−i2i200
χ4122-2-2-22-222-2-22000022-22-2-22-20000000000-2-220002022-2-2-22-222−2−22000000000022−2−2−2−2220000000000000000002−2−2200
χ4222-2-2-22-222-2-22000022-22-2-22-20000000000-2-220002022-2-2-22-22−222−20000000000−2−22222−2−2000000000000000000−222−200
χ4322-2-2-22-222-2-22000022-22-2-22-20000000000-2-2200020-2-2222-22-22−2−22000000000022−2−2−2−222000000000000000000−222−200
χ4422-2-2-22-222-2-22000022-22-2-22-20000000000-2-2200020-2-2222-22-2−222−20000000000−2−22222−2−20000000000000000002−2−2200
χ452-2-222-2-22200022-2-20-2-2222-2-200−i2i2−i2i2−i2i2−i2i200022-20-22-22-20000000000−i2i2−i2i2−i2i2−i2i200000000002-2−i2i2−i2i2−i2i2−i2i2000000000000
χ462-2-222-2-22200022-2-20-2-2222-2-200−i2i2−i2i2−i2i2−i2i200022-20-2-22-220000000000−i2i2−i2i2−i2i2−i2i20000000000-22i2−i2i2−i2i2−i2i2−i2000000000000
χ472-2-222-2-22200022-2-20-2-2222-2-200i2−i2i2−i2i2−i2i2−i200022-20-22-22-20000000000i2−i2i2−i2i2−i2i2−i200000000002-2i2−i2i2−i2i2−i2i2−i2000000000000
χ482-2-222-2-22200022-2-20-2-2222-2-200i2−i2i2−i2i2−i2i2−i200022-20-2-22-220000000000i2−i2i2−i2i2−i2i2−i20000000000-22−i2i2−i2i2−i2i2−i2i2000000000000
χ492-2-222-2-222000-2-2220-2-2222-2-2002−22−2−22−22000-2-22022-22-200000000002−22−2−22−220000000000-222−22−2−22−22000000000000
χ502-2-222-2-222000-2-2220-2-2222-2-2002−22−2−22−22000-2-2202-22-2200000000002−22−2−22−2200000000002-2−22−222−22−2000000000000
χ512-2-222-2-222000-2-2220-2-2222-2-200−22−222−22−2000-2-22022-22-20000000000−22−222−22−20000000000-22−22−222−22−2000000000000
χ522-2-222-2-222000-2-2220-2-2222-2-200−22−222−22−2000-2-2202-22-220000000000−22−222−22−200000000002-22−22−2−22−22000000000000
χ532-2-2-2222-222-222-2-22-2-2-2-2-22222-22i−2i−2i2i2i−2i−2i2i2-222-22-2-20000000000002-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000
χ542-2-2-2222-222-222-2-22-2-2-2-2-22222-2−2i2i2i−2i−2i2i2i−2i2-222-22-2-20000000000002-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000
χ552-2-2-2222-222-22-222-2-2-2-2-2-2222-22000000002-22-22-2-22000000000000-22000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ562-2-2-2222-222-22-222-2-2-2-2-2-2222-22000000002-22-22-2-22000000000000-2200000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ572-2-2-2222-22-22-22-2-222-2-2-2-2222-2200000000-22-22-222-2000000000000-22000000000000000000002-2-222-2-22000000000000
χ582-2-2-2222-22-22-22-2-222-2-2-2-2222-2200000000-22-22-222-2000000000000-2200000000000000000000-222-2-222-2000000000000
χ592-2-2-2222-22-22-2-222-22-2-2-2-22222-22-2-22-222-2-22-2-22-2220000000000002-22-2-22-222-200000000000000000000000000000000
χ602-2-2-2222-22-22-2-222-22-2-2-2-22222-2-222-22-2-22-22-2-22-2220000000000002-2-222-22-2-2200000000000000000000000000000000
χ612-2-2-2222-2-12-222-2-22-21111-1-1-12-22i−2i−2i2i2i−2i−2i2i-11-1-11-111000000000000-11−iii−i−iii−i3−33−33−33−300000000000000−i3i3−i3i3000000
χ622-2-2-2222-2-12-222-2-22-21111-1-1-12-22i−2i−2i2i2i−2i−2i2i-11-1-11-111000000000000-11−iii−i−iii−i−33−33−33−3300000000000000i3−i3i3−i3000000
χ632-2-2-2222-2-12-222-2-22-21111-1-1-12-2−2i2i2i−2i−2i2i2i−2i-11-1-11-111000000000000-11i−i−iii−i−ii3−33−33−33−300000000000000i3−i3i3−i3000000
χ642-2-2-2222-2-12-222-2-22-21111-1-1-12-2−2i2i2i−2i−2i2i2i−2i-11-1-11-111000000000000-11i−i−iii−i−ii−33−33−33−3300000000000000−i3i3−i3i3000000
χ652-2-2-2222-2-1-22-2-222-221111-1-1-12-22-2-22-222-21-111-11-1-1000000000000-11-111-11-1-11−i3i3−i3i3i3−i3i3−i300000000000000−i3i3i3−i3000000
χ662-2-2-2222-2-1-22-2-222-221111-1-1-12-22-2-22-222-21-111-11-1-1000000000000-11-111-11-1-11i3−i3i3−i3−i3i3−i3i300000000000000i3−i3−i3i3000000
χ672-2-2-2222-2-1-22-2-222-221111-1-1-12-2-222-22-2-221-111-11-1-1000000000000-111-1-11-111-1−i3i3−i3i3i3−i3i3−i300000000000000i3−i3−i3i3000000
χ682-2-2-2222-2-1-22-2-222-221111-1-1-12-2-222-22-2-221-111-11-1-1000000000000-111-1-11-111-1i3−i3i3−i3−i3i3−i3i300000000000000−i3i3i3−i3000000
χ6944444444-2444-4-4-4-44-2-2-2-2-2-2-2-4-400000000-2-2-2222-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-400000000222-2-2-22-2000000000000220000000000000000000000000000000000000000
χ71444-44-4-4-4-20004-44-40-2-222-222002222−22−222222−22−22000-2220-200000000000000−2−222−2−22200000000000000000000000000000000
χ72444-44-4-4-4-20004-44-40-2-222-22200−22−222222−22−222222000-2220-20000000000000022−2−222−2−200000000000000000000000000000000
χ73444-44-4-4-4-2000-44-440-2-222-22200−2i2−2i22i22i22i22i2−2i2−2i20002-2-20200000000000000i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ74444-44-4-4-4-2000-44-440-2-222-222002i22i2−2i2−2i2−2i2−2i22i22i20002-2-20200000000000000−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ7544-44-4-44-44000000004-4-44-4-4400000000000000000000004i−4i−4i4i0000000000000000000000000000000000000000000000
χ7644-44-4-44-44000000004-4-44-4-440000000000000000000000−4i4i4i−4i0000000000000000000000000000000000000000000000
χ7744-4-4-44-44-244-40000-4-22-222-220000000000-2-220002000000000−2i22i2−2i22i20000000000i2i2−i2−i2i2i2−i2−i2000000000000000000000000
χ7844-4-4-44-44-244-40000-4-22-222-220000000000-2-2200020000000002i2−2i22i2−2i20000000000−i2−i2i2i2−i2−i2i2i2000000000000000000000000
χ7944-4-4-44-44-2-4-4400004-22-222-22000000000022-2000-200000000022−22−22220000000000−2−22222−2−2000000000000000000000000
χ8044-4-4-44-44-2-4-4400004-22-222-22000000000022-2000-2000000000−222222−22000000000022−2−2−2−222000000000000000000000000
χ814-444-44-4-444-4-400004-44-44-44-400000000004-4-400040000000000000000000000000000000000000000000000000000000
χ824-444-44-4-44-4440000-4-44-44-44-40000000000-444000-40000000000000000000000000000000000000000000000000000000
χ834-444-44-4-4-24-4-4000042-22-22-220000000000-222000-200000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ844-444-44-4-4-24-4-4000042-22-22-220000000000-222000-200000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ854-444-44-4-4-2-4440000-42-22-22-2200000000002-2-20002000000000000000000000006−6−66−666−6000000000000000000000000
χ864-444-44-4-4-2-4440000-42-22-22-2200000000002-2-2000200000000000000000000000−666−66−6−66000000000000000000000000
χ874-44-4-4-444400000000-444-4-4-440000000000000000004-4-4400000000000000000000000000000000000000000000000000
χ884-44-4-4-444400000000-444-4-4-44000000000000000000-444-400000000000000000000000000000000000000000000000000
χ894-4-444-4-44-200044-4-4022-2-2-22200−2i22i2−2i22i2−2i22i2−2i22i2000-2-220200000000000000i2−i2i2−i2i2−i2i2−i200000000000000000000000000000000
χ904-4-444-4-44-200044-4-4022-2-2-222002i2−2i22i2−2i22i2−2i22i2−2i2000-2-220200000000000000−i2i2−i2i2−i2i2−i2i200000000000000000000000000000000
χ914-4-444-4-44-2000-4-444022-2-2-2220022−2222−22−2222−222200022-20-200000000000000−22−222−22−200000000000000000000000000000000
χ924-4-444-4-44-2000-4-444022-2-2-22200−2222−222222−2222−2200022-20-2000000000000002−22−2−22−2200000000000000000000000000000000
χ934-4-4-4444-4-24-44-444-4-42222-2-2-2-4400000000-22-22-222-20000000000002-20000000000000000000000000000000000000000
χ944-4-4-4444-4-2-44-44-4-4442222-2-2-2-44000000002-22-22-2-220000000000002-20000000000000000000000000000000000000000
χ9588-88-8-88-8-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-8-888-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000

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