Finite Group Databasebeta

← Group #10693531

Character table — Group #10693531

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order122222223444444446666666444444444412121212121212128888888888881212121212121212121224242424242424248888888888884412121212888844
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
χ91-111-1-11-1111-1-1-1-111-1-111-1-111-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−iii−i−i1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i1111-1-1-1-11-111-1-111-1-1i−i
χ101-111-1-11-1111-1-1-1-111-1-111-1-111-1iiii−i−i−i−i11-1-111-1-1iiii−i−i−i−i−i−iii1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i1111-1-1-1-1-11-1-111-1-111−ii
χ111-111-1-11-1111-1-1-1-111-1-111-1-111-1iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiiiii−i−i1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii-1-1-1-111111-111-1-1-1-111−ii
χ121-111-1-11-1111-1-1-1-111-1-111-1-111-1iiii−i−i−i−i11-1-111-1-1−i−i−i−iiiii−i−iii1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-1-1-11111-11-1-11111-1-1i−i
χ131-111-1-11-1111-1-1-1-111-1-111-1-111-1−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−iii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-1-1-11111-11-1-11111-1-1−ii
χ141-111-1-11-1111-1-1-1-111-1-111-1-111-1−i−i−i−iiiii11-1-111-1-1iiii−i−i−i−i−i−iii1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−i-1-1-1-111111-111-1-1-1-111i−i
χ151-111-1-11-1111-1-1-1-111-1-111-1-111-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiiiii−i−i1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iii1111-1-1-1-1-11-1-111-1-111i−i
χ161-111-1-11-1111-1-1-1-111-1-111-1-111-1−i−i−i−iiiii11-1-111-1-1−i−i−i−iiiii−i−iii1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii1111-1-1-1-11-111-1-111-1-1−ii
χ172222222222-2-2-2222-22222222-2-2000000002222-2-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ182222222222-2-2-2222-22222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2222-2-2-222222222-2-222-2-222-2-2-2-2-2-22222000000000000-2-222-2-222-2-200000000000000000000000000000000
χ20222222222-2222-2-2-222222222-2-2-2-222-2-222-2-2-2-22222000000000000-2-2-2-222-2-22200000000000000000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-200000000000022000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-222222222200000000-2-2-2-2-2-2-2-20000000000002200000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
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
χ2722222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-100000000000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-21111-1-1-1-100000000000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-10000000000001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1-2222-2-2-22-1-1-1-1-1-1-1-2-2-2-222-2-2221111-1-1-1-10000000000001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-2-2-2-222-20002-220222-2-2-2-200000000002-22-200002i2i−2i−2i2i2i−2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ32222-2-2-2-222-20002-220222-2-2-2-200000000002-22-200002i2i−2i−2i2i2i−2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ33222-2-2-2-222-20002-220222-2-2-2-200000000002-22-20000−2i−2i2i2i−2i−2i2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ34222-2-2-2-222-20002-220222-2-2-2-200000000002-22-20000−2i−2i2i2i−2i−2i2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ3522-2-22-22-2202-22000-22-2-2-22-2200002-2002-200002-2-22−i2i2−i2i2−i2i2−i2i2000000002-2002-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3622-2-22-22-2202-22000-22-2-2-22-2200002-2002-200002-2-22i2−i2i2−i2i2−i2i2−i2000000002-2002-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3722-2-22-22-2202-22000-22-2-2-22-220000-2200-2200002-2-22−i2i2−i2i2−i2i2−i2i200000000-2200-2200000000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-2-22-22-2202-22000-22-2-2-22-220000-2200-2200002-2-22i2−i2i2−i2i2−i2i2−i200000000-2200-2200000000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-2-22-22-220-22-200022-2-2-22-22002i−2i002i−2i000000-222-2−i2i2−i2i2−i2i2−i2i20000002i−2i002i−2i0000000000i2−i2i2−i22−2−222−2−22000000000000
χ4022-2-22-22-220-22-200022-2-2-22-22002i−2i002i−2i000000-222-2i2−i2i2−i2i2−i2i2−i20000002i−2i002i−2i0000000000−i2i2−i2i2−222−2−222−2000000000000
χ4122-2-22-22-220-22-200022-2-2-22-2200−2i2i00−2i2i000000-222-2−i2i2−i2i2−i2i2−i2i2000000−2i2i00−2i2i0000000000i2−i2i2−i2−222−2−222−2000000000000
χ4222-2-22-22-220-22-200022-2-2-22-2200−2i2i00−2i2i000000-222-2i2−i2i2−i2i2−i2i2−i2000000−2i2i00−2i2i0000000000−i2i2−i2i22−2−222−2−22000000000000
χ432-222-2-22-222-222-2-22-2-2-222-2-22-220000000022-2-2-2-2222i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ442-222-2-22-222-222-2-22-2-2-222-2-22-220000000022-2-2-2-222−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ452-222-2-22-22-22-2-222-22-2-222-2-22-222i2i−2i−2i−2i−2i2i2i-2-22222-2-2000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ462-222-2-22-22-22-2-222-22-2-222-2-22-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ472-222-2-22-22-2-22222-2-2-2-222-2-222-200000000-2-222-2-2220000000000002-2000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ482-222-2-22-22-2-22222-2-2-2-222-2-222-200000000-2-222-2-2220000000000002-200000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ492-222-2-22-2-122-2-2-2-22211-1-111-12-22i2i2i2i−2i−2i−2i−2i-1-111-1-111000000002i2i−2i−2i-11−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-111000000
χ502-222-2-22-2-122-2-2-2-22211-1-111-12-22i2i2i2i−2i−2i−2i−2i-1-111-1-11100000000−2i−2i2i2i-11−i−i−i−iiiiiiiii−i−i−i−i000000000000-2211-1-1000000
χ512-222-2-22-2-122-2-2-2-22211-1-111-12-2−2i−2i−2i−2i2i2i2i2i-1-111-1-111000000002i2i−2i−2i-11iiii−i−i−i−i−i−i−i−iiiii000000000000-2211-1-1000000
χ522-222-2-22-2-122-2-2-2-22211-1-111-12-2−2i−2i−2i−2i2i2i2i2i-1-111-1-11100000000−2i−2i2i2i-11iiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-111000000
χ532-222-2-22-2-1-22-2-222-2211-1-111-1-222i2i−2i−2i−2i−2i2i2i11-1-1-1-1110000000000001-1−i−iiiii−i−i33−3−3−3−33300000000000000−i3i3i3−i3000000
χ542-222-2-22-2-1-22-2-222-2211-1-111-1-222i2i−2i−2i−2i−2i2i2i11-1-1-1-1110000000000001-1−i−iiiii−i−i−3−33333−3−300000000000000i3−i3−i3i3000000
χ552-222-2-22-2-1-22-2-222-2211-1-111-1-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-1110000000000001-1ii−i−i−i−iii33−3−3−3−33300000000000000i3−i3−i3i3000000
χ562-222-2-22-2-1-22-2-222-2211-1-111-1-22−2i−2i2i2i2i2i−2i−2i11-1-1-1-1110000000000001-1ii−i−i−i−iii−3−33333−3−300000000000000−i3i3i3−i3000000
χ572-22-222-2-22-2000-2220-2-22-222-200000000002-2-22000022-2-2-2-222−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−i2i2i2−i200
χ582-22-222-2-22-2000-2220-2-22-222-200000000002-2-22000022-2-2-2-222i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000i2−i2−i2i200
χ592-22-222-2-22-2000-2220-2-22-222-200000000002-2-220000-2-22222-2-2−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000i2−i2−i2i200
χ602-22-222-2-22-2000-2220-2-22-222-200000000002-2-220000-2-22222-2-2i2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−i2i2i2−i200
χ612-2-2-2-22222022-2000-2-22-2-2-22200002i−2i00−2i2i00002-22-22−22−2−22−22000000002i−2i00−2i2i000000002−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ622-2-2-2-22222022-2000-2-22-2-2-22200002i−2i00−2i2i00002-22-2−22−222−22−2000000002i−2i00−2i2i00000000−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ632-2-2-2-22222022-2000-2-22-2-2-2220000−2i2i002i−2i00002-22-22−22−2−22−2200000000−2i2i002i−2i000000002−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ642-2-2-2-22222022-2000-2-22-2-2-2220000−2i2i002i−2i00002-22-2−22−222−22−200000000−2i2i002i−2i00000000−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ652-2-2-2-222220-2-220002-22-2-2-222002-200-22000000-22-222−22−2−22−220000002-200-220000000000−222−2−222−22−2−22000000000000
χ662-2-2-2-222220-2-220002-22-2-2-222002-200-22000000-22-22−22−222−22−20000002-200-2200000000002−2−222−2−22−222−2000000000000
χ672-2-2-2-222220-2-220002-22-2-2-22200-22002-2000000-22-222−22−2−22−22000000-22002-20000000000−222−22−2−22−222−2000000000000
χ682-2-2-2-222220-2-220002-22-2-2-22200-22002-2000000-22-22−22−222−22−2000000-22002-200000000002−2−22−222−22−2−22000000000000
χ6944444444-24-4-4-4444-4-2-2-2-2-2-2-2-4-400000000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-4-4-4-4444000-44-40444-4-4-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-24000-44-40-2-2-2222200000000002-22-200000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ73444-4-4-4-44-24000-44-40-2-2-2222200000000002-22-200000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ74444-4-4-4-44-2-40004-440-2-2-222220000000000-22-2200000000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ75444-4-4-4-44-2-40004-440-2-2-222220000000000-22-22000000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7644-44-44-4-44000000004-4-44-44-400000000000000000022−22−222222−22−22220000000000000000000000000000000000000000000000
χ7744-44-44-4-44000000004-4-44-44-4000000000000000000−222222−22−222222−220000000000000000000000000000000000000000000000
χ7844-4-44-44-4-204-44000-4-2222-22-200004-4004-40000-222-20000000000000000-2200-2200000000000000000000000000000000
χ7944-4-44-44-4-204-44000-4-2222-22-20000-4400-440000-222-200000000000000002-2002-200000000000000000000000000000000
χ8044-4-44-44-4-20-44-40004-2222-22-2004i−4i004i−4i0000002-2-2200000000000000−2i2i00−2i2i0000000000000000000000000000000000
χ8144-4-44-44-4-20-44-40004-2222-22-200−4i4i00−4i4i0000002-2-22000000000000002i−2i002i−2i0000000000000000000000000000000000
χ824-444-4-44-4-24-444-4-44-422-2-222-2-4400000000-2-22222-2-20000000000002-20000000000000000000000000000000000000000
χ834-444-4-44-4-2-4-44444-4-422-2-222-24-40000000022-2-222-2-2000000000000-220000000000000000000000000000000000000000
χ844-44-444-4-4440004-4-40-4-44-444-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ854-44-444-4-4-240004-4-4022-22-2-2200000000002-2-22000000000000000000000000006−6−66−666−6000000000000000000000000
χ864-44-444-4-4-240004-4-4022-22-2-2200000000002-2-2200000000000000000000000000−666−66−6−66000000000000000000000000
χ874-44-444-4-4-2-4000-444022-22-2-220000000000-222-2000000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ884-44-444-4-4-2-4000-444022-22-2-220000000000-222-20000000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ894-4-444-4-44400000000-44-444-4-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ904-4-444-4-44400000000-44-444-4-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ914-4-4-4-4444-2044-4000-42-2222-2-200004i−4i00−4i4i0000-22-220000000000000000−2i2i002i−2i00000000000000000000000000000000
χ924-4-4-4-4444-2044-4000-42-2222-2-20000−4i4i004i−4i0000-22-2200000000000000002i−2i00−2i2i00000000000000000000000000000000
χ934-4-4-4-4444-20-4-4400042-2222-2-2004-400-440000002-22-200000000000000-22002-20000000000000000000000000000000000
χ944-4-4-4-4444-20-4-4400042-2222-2-200-44004-40000002-22-2000000000000002-200-220000000000000000000000000000000000
χ9588-88-88-8-8-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-888-8-88-4000000004-44-4-444000000000000000000000000000000000000000000000000000000000000000000000000

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