Finite Group Databasebeta

← Group #10693846

Character table — Group #10693846

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
χ91-1111-1-1-111-1-1-111-11-1111-1-1-11-1ii−i−iii−i−i111-1-1-1-111111-1-1-1-111-1-11-1iiii−i−i−i−i1111-1-1-1-111-1-1iiii−i−i−i−ii−iii−i−i11-1-1i−i
χ101-1111-1-1-111-1-1-111-11-1111-1-1-11-1ii−i−iii−i−i111-1-1-1-111111-1-1-1-1-1-1111-1iiii−i−i−i−i-1-1-1-1111111-1-1iiii−i−i−i−i−ii−i−iii-1-111−ii
χ111-1111-1-1-111-1-1-111-11-1111-1-1-11-1ii−i−iii−i−i111-1-1-1-11-1-1-1-1111111-1-11-1iiii−i−i−i−i1111-1-1-1-1-1-111−i−i−i−iiiiii−iii−i−i-1-111−ii
χ121-1111-1-1-111-1-1-111-11-1111-1-1-11-1ii−i−iii−i−i111-1-1-1-11-1-1-1-11111-1-1111-1iiii−i−i−i−i-1-1-1-11111-1-111−i−i−i−iiiii−ii−i−iii11-1-1i−i
χ131-1111-1-1-111-1-1-111-11-1111-1-1-11-1−i−iii−i−iii111-1-1-1-111111-1-1-1-111-1-11-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−i−i−iiiii−ii−i−iii11-1-1−ii
χ141-1111-1-1-111-1-1-111-11-1111-1-1-11-1−i−iii−i−iii111-1-1-1-111111-1-1-1-1-1-1111-1−i−i−i−iiiii-1-1-1-1111111-1-1−i−i−i−iiiiii−iii−i−i-1-111i−i
χ151-1111-1-1-111-1-1-111-11-1111-1-1-11-1−i−iii−i−iii111-1-1-1-11-1-1-1-1111111-1-11-1−i−i−i−iiiii1111-1-1-1-1-1-111iiii−i−i−i−i−ii−i−iii-1-111i−i
χ161-1111-1-1-111-1-1-111-11-1111-1-1-11-1−i−iii−i−iii111-1-1-1-11-1-1-1-11111-1-1111-1−i−i−i−iiiii-1-1-1-11111-1-111iiii−i−i−i−ii−iii−i−i11-1-1−ii
χ17222222222222-2-2-2-222222222-2-22222-2-2-2-22-2-222-2-22000000000000-2-222-2-222-2-200000000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-2-2-2-2-222222-2-222-2-22000000000000-2-2-2-222-2-22200000000000000000000000000000000
χ19222222222-2-2-22222-22222222-2-200000000-222-2-222-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ20222222222-2-2-22222-22222222-2-200000000-222-2-222-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
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
χ2722222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-2-111-1-111-100000000000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-22222-2-2-2-2-111-1-111-100000000000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-22222-111-1-111-10000000000001111-1-111-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-2-2-2-2-22222-111-1-111-10000000000001111-1-111-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-2-22-2-2222-20000-222-2-22-2-2002-22-200002002-200-222−2−222−2−20000002-2002-200000000002−22−22−22−22−22−2000000000000
χ32222-2-22-2-2222-20000-222-2-22-2-2002-22-200002002-200-2−2−222−2−2220000002-2002-20000000000−22−22−22−22−22−22000000000000
χ33222-2-22-2-2222-20000-222-2-22-2-200-22-2200002002-200-222−2−222−2−2000000-2200-2200000000002−22−2−22−22−22−22000000000000
χ34222-2-22-2-2222-20000-222-2-22-2-200-22-2200002002-200-2−2−222−2−222000000-2200-220000000000−22−222−22−22−22−2000000000000
χ35222-2-22-2-22-2-220000222-2-22-2-20000002i−2i2i−2i-200-2200222−2−222−2−2000000002i−2i002i−2i00000000−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ36222-2-22-2-22-2-220000222-2-22-2-20000002i−2i2i−2i-200-22002−2−222−2−222000000002i−2i002i−2i000000002−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ37222-2-22-2-22-2-220000222-2-22-2-2000000−2i2i−2i2i-200-2200222−2−222−2−200000000−2i2i00−2i2i00000000−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ38222-2-22-2-22-2-220000222-2-22-2-2000000−2i2i−2i2i-200-22002−2−222−2−22200000000−2i2i00−2i2i000000002−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ3922-22-2-22-22000-22-2202-22-2-2-22000000000002-2002-202i−2i2i−2i2i−2i2i−2i−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i20000000000000000002−22−200
χ4022-22-2-22-22000-22-2202-22-2-2-22000000000002-2002-202i−2i2i−2i2i−2i2i−2ii2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000−22−2200
χ4122-22-2-22-22000-22-2202-22-2-2-22000000000002-2002-20−2i2i−2i2i−2i2i−2i2i−i2i2−i2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000−22−2200
χ4222-22-2-22-22000-22-2202-22-2-2-22000000000002-2002-20−2i2i−2i2i−2i2i−2i2ii2−i2i2−i20000000000i2−i2i2−i2i2−i2i2−i20000000000000000002−22−200
χ432-2222-2-2-222-2-22-2-222-2222-2-2-2-222i2i−2i−2i−2i−2i2i2i2-2-2-2-2222000000000000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ442-2222-2-2-222-2-22-2-222-2222-2-2-2-22−2i−2i2i2i2i2i−2i−2i2-2-2-2-2222000000000000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ452-2222-2-2-22-2222-2-22-2-2222-2-2-22-200000000-2-2-22222-20000000000002-20000000000000000000022-2-2-2-222000000000000
χ462-2222-2-2-22-2222-2-22-2-2222-2-2-22-200000000-2-2-22222-20000000000002-200000000000000000000-2-22222-2-2000000000000
χ472-2222-2-2-22-222-222-2-2-2222-2-2-2-2200000000-22222-2-2-22222-2-2-2-20000-220000000000000000-2-22200000000000000000000
χ482-2222-2-2-22-222-222-2-2-2222-2-2-2-2200000000-22222-2-2-2-2-2-2-222220000-22000000000000000022-2-200000000000000000000
χ492-2222-2-2-2-12-2-22-2-2221-1-1-1111-222i2i−2i−2i−2i−2i2i2i-11111-1-1-10000000000001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000003−3−33000000
χ502-2222-2-2-2-12-2-22-2-2221-1-1-1111-222i2i−2i−2i−2i−2i2i2i-11111-1-1-10000000000001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000000−333−3000000
χ512-2222-2-2-2-12-2-22-2-2221-1-1-1111-22−2i−2i2i2i2i2i−2i−2i-11111-1-1-10000000000001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000000−333−3000000
χ522-2222-2-2-2-12-2-22-2-2221-1-1-1111-22−2i−2i2i2i2i2i−2i−2i-11111-1-1-10000000000001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000003−3−33000000
χ532-2222-2-2-2-12-2-2-222-221-1-1-11112-22i2i−2i−2i2i2i−2i−2i-1-1-11111-10000000022-2-2-11−i−i−i−iiiii-1-1-1-111110000000000002i−2i−i−iii000000
χ542-2222-2-2-2-12-2-2-222-221-1-1-11112-22i2i−2i−2i2i2i−2i−2i-1-1-11111-100000000-2-222-11−i−i−i−iiiii1111-1-1-1-1000000000000−2i2iii−i−i000000
χ552-2222-2-2-2-12-2-2-222-221-1-1-11112-2−2i−2i2i2i−2i−2i2i2i-1-1-11111-10000000022-2-2-11iiii−i−i−i−i-1-1-1-11111000000000000−2i2iii−i−i000000
χ562-2222-2-2-2-12-2-2-222-221-1-1-11112-2−2i−2i2i2i−2i−2i2i2i-1-1-11111-100000000-2-222-11iiii−i−i−i−i1111-1-1-1-10000000000002i−2i−i−iii000000
χ572-22-2-2-22222-220000-2-22-2-2-222002i−2i−2i2i0000200-2200-222−2−2−2−2220000002i−2i00−2i2i00000000002−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ582-22-2-2-22222-220000-2-22-2-2-222002i−2i−2i2i0000200-2200-2−2−22222−2−20000002i−2i00−2i2i0000000000−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ592-22-2-2-22222-220000-2-22-2-2-22200−2i2i2i−2i0000200-2200-222−2−2−2−222000000−2i2i002i−2i00000000002−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ602-22-2-2-22222-220000-2-22-2-2-22200−2i2i2i−2i0000200-2200-2−2−22222−2−2000000−2i2i002i−2i0000000000−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ612-22-2-2-2222-22-200002-22-2-2-2220000002-2-22-2002-200222−2−2−2−222000000002-200-2200000000−222−2−222−22−2−22000000000000
χ622-22-2-2-2222-22-200002-22-2-2-2220000002-2-22-2002-2002−2−22222−2−2000000002-200-22000000002−2−222−2−22−222−2000000000000
χ632-22-2-2-2222-22-200002-22-2-2-222000000-222-2-2002-200222−2−2−2−22200000000-22002-200000000−222−22−2−22−222−2000000000000
χ642-22-2-2-2222-22-200002-22-2-2-222000000-222-2-2002-2002−2−22222−2−200000000-22002-2000000002−2−22−222−22−2−22000000000000
χ652-2-22-22-22200022-2-20-2-22-222-2000000000002-200-2202i−2i2i−2i−2i2i−2i2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ662-2-22-22-22200022-2-20-2-22-222-2000000000002-200-2202i−2i2i−2i−2i2i−2i2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ672-2-22-22-22200022-2-20-2-22-222-2000000000002-200-220−2i2i−2i2i2i−2i2i−2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ682-2-22-22-22200022-2-20-2-22-222-2000000000002-200-220−2i2i−2i2i2i−2i2i−2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ6944444444-2-4-4-44444-4-2-2-2-2-2-2-2-4-4000000002-2-222-2-22000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-4-44-4-4-244-40000-4-2-222-222004-44-40000-200-2200200000000000000-2200-220000000000000000000000000000000000
χ72444-4-44-4-4-244-40000-4-2-222-22200-44-440000-200-22002000000000000002-2002-20000000000000000000000000000000000
χ73444-4-44-4-4-2-4-4400004-2-222-2220000004i−4i4i−4i2002-200-20000000000000000−2i2i00−2i2i00000000000000000000000000000000
χ74444-4-44-4-4-2-4-4400004-2-222-222000000−4i4i−4i4i2002-200-200000000000000002i−2i002i−2i00000000000000000000000000000000
χ7544-44-4-44-440004-44-404-44-4-4-4400000000000-4400-440000000000000000000000000000000000000000000000000000000
χ7644-44-4-44-4-20004-44-40-22-2222-2000000000002-2002-2000000000000000000000006−6−666−6−66000000000000000000000000
χ7744-44-4-44-4-20004-44-40-22-2222-2000000000002-2002-200000000000000000000000−666−6−666−6000000000000000000000000
χ7844-44-4-44-4-2000-44-440-22-2222-200000000000-2200-22000000000−2i22i2−2i22i20000000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ7944-44-4-44-4-2000-44-440-22-2222-200000000000-2200-220000000002i2−2i22i2−2i20000000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ8044-4-44-4-444000000004-4-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ8144-4-44-4-444000000004-4-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ824-4444-4-4-4-2-4444-4-44-42-2-2-22224-400000000222-2-2-2-22000000000000-220000000000000000000000000000000000000000
χ834-4444-4-4-4-2-444-444-4-42-2-2-2222-44000000002-2-2-2-22220000000000002-20000000000000000000000000000000000000000
χ844-44-4-4-444-24-440000-42-2222-2-2004i−4i−4i4i0000-2002-200200000000000000−2i2i002i−2i0000000000000000000000000000000000
χ854-44-4-4-444-24-440000-42-2222-2-200−4i4i4i−4i0000-2002-2002000000000000002i−2i00−2i2i0000000000000000000000000000000000
χ864-44-4-4-444-2-44-4000042-2222-2-20000004-4-44200-2200-20000000000000000-22002-200000000000000000000000000000000
χ874-44-4-4-444-2-44-4000042-2222-2-2000000-444-4200-2200-200000000000000002-200-2200000000000000000000000000000000
χ884-4-44-44-444000-4-4440-4-44-444-400000000000-44004-40000000000000000000000000000000000000000000000000000000
χ894-4-44-44-44-200044-4-4022-22-2-2200000000000-22002-2000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ904-4-44-44-44-200044-4-4022-22-2-2200000000000-22002-20000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ914-4-44-44-44-2000-4-444022-22-2-22000000000002-200-22000000000000000000000006−6−66−666−6000000000000000000000000
χ924-4-44-44-44-2000-4-444022-22-2-22000000000002-200-2200000000000000000000000−666−66−6−66000000000000000000000000
χ934-4-4-4444-4400000000-4-4-444-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ944-4-4-4444-4400000000-4-4-444-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ9588-8-88-8-88-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-8-8-8888-8-400000000444-4-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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