Finite Group Databasebeta

← Group #10691328

Character table — Group #10691328

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111112222222222222222444444444444444444666666668888888888888888888888121212121212121212121212161616161616242424244848
order12222222344444444666666622224444441212121212121212888888886666888812121212121224242424242424248888888888884412121212888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ91-1-1-1111-111-1111-1-1-1-1-1-1-111111-1-111-1-11-11-1-111-1-11iiii−i−i−i−i11-1-111-1-111-1-11-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−ii−i
χ101-1-1-1111-111-1111-1-1-1-1-1-1-111111-1-111-1-11-11-1-111-1-11iiii−i−i−i−i11-1-1-1-11111-1-11-1-1-1-1-11111ii−i−iiiii−i−i−i−i-11-1-111−i−iii−ii
χ111-1-1-1111-111-1111-1-1-1-1-1-1-111111-1-111-1-11-11-1-111-1-11−i−i−i−iiiii11-1-111-1-111-1-11-11111-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii−ii
χ121-1-1-1111-111-1111-1-1-1-1-1-1-111111-1-111-1-11-11-1-111-1-11−i−i−i−iiiii11-1-1-1-11111-1-11-1-1-1-1-11111−i−iii−i−i−i−iiiii-11-1-111ii−i−ii−i
χ131-1-1-1111-111-1111-1-1-1-1-1-1-1111-1-111-1-1111-11-1-111-1-11iiii−i−i−i−i-1-11111-1-1-1-1111-11111-1-1-1-1ii−i−i−i−i−i−iiiii-11-1-111ii−i−i−ii
χ141-1-1-1111-111-1111-1-1-1-1-1-1-1111-1-111-1-1111-11-1-111-1-11iiii−i−i−i−i-1-111-1-111-1-1111-1-1-1-1-11111ii−i−i−i−i−i−iiiii1-111-1-1−i−iiii−i
χ151-1-1-1111-111-1111-1-1-1-1-1-1-1111-1-111-1-1111-11-1-111-1-11−i−i−i−iiiii-1-11111-1-1-1-1111-11111-1-1-1-1−i−iiiiiii−i−i−i−i-11-1-111−i−iiii−i
χ161-1-1-1111-111-1111-1-1-1-1-1-1-1111-1-111-1-1111-11-1-111-1-11−i−i−i−iiiii-1-111-1-111-1-1111-1-1-1-1-11111−i−iiiiiii−i−i−i−i1-111-1-1ii−i−i−ii
χ1722222222222-2-22-22-222222222222-2-2-2-2-2-2222-2-2-2-220000000022220000-2-2-2-2-2-200000000000000000000000000000000
χ1822222222222-2-22-22-22222222-2-2-2-22222-2-2222-2-2-2-2200000000-2-2-2-200002222-2-200000000000000000000000000000000
χ19222222222-2-222-22-22222222200000000-2-2-2-2-22222-222222222000000000000-2-200000000-2-2-2-200000000000000000000
χ20222222222-2-222-22-22222222200000000-2-2-2-2-22222-2-2-2-2-2-2-2-2-2000000000000-2-200000000222200000000000000000000
χ21222222222-2-2-2-2-2-2-2-222222220000000022-2-2-2-2-2-2-2-200000000000000000000220000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ22222222222-2-2-2-2-2-2-2-222222220000000022-2-2-2-2-2-2-2-20000000000000000000022000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
χ2422222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-100000000-1-1-1-1-2-2-2-2-1-1-1-1-1-111111111000000000000-2-21111000000
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-100000000111122221111-1-1-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-1000000001111-2-2-2-21111-1-11111111100000000000022-1-1-1-1000000
χ2722222222-122-2-22-22-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-100000000-1-1-1-10000111111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-122-2-22-22-2-1-1-1-1-1-1-12222-2-2-2-2-2-2-1-1-11111-100000000-1-1-1-10000111111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-2-22222-2-2-1-1-11111-10000000011110000-1-1-1-111−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-122-2-22-22-2-1-1-1-1-1-1-1-2-2-2-22222-2-2-1-1-11111-10000000011110000-1-1-1-111i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-22-2-2-222200-20-2022-2-22-2-22-22-200000022-20000-222−2−222−2−22-22-20000000000000000002−22−22−22−22−22−2000000000000
χ32222-22-2-2-222200-20-2022-2-22-2-22-22-200000022-20000-2−2−222−2−2222-22-2000000000000000000−22−22−22−22−22−22000000000000
χ33222-22-2-2-222200-20-2022-2-22-2-2-22-2200000022-20000-222−2−222−2−2-22-220000000000000000002−22−2−22−22−22−22000000000000
χ34222-22-2-2-222200-20-2022-2-22-2-2-22-2200000022-20000-2−2−222−2−222-22-22000000000000000000−22−222−22−22−22−2000000000000
χ35222-22-2-2-22-2-200202022-2-22-2-200002i−2i2i−2i00-2-220000222−2−222−2−2000000002i−2i2i−2i0000000000−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ36222-22-2-2-22-2-200202022-2-22-2-200002i−2i2i−2i00-2-2200002−2−222−2−222000000002i−2i2i−2i00000000002−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ37222-22-2-2-22-2-200202022-2-22-2-20000−2i2i−2i2i00-2-220000222−2−222−2−200000000−2i2i−2i2i0000000000−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ38222-22-2-2-22-2-200202022-2-22-2-20000−2i2i−2i2i00-2-2200002−2−222−2−22200000000−2i2i−2i2i00000000002−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ3922-22-22-2-22002-20-2022-22-2-22-200000000000002-22-202-22-22-22-20000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000−i2i2−i2i200
χ4022-22-22-2-22002-20-2022-22-2-22-200000000000002-22-202-22-22-22-20000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000i2−i2i2−i200
χ4122-22-22-2-22002-20-2022-22-2-22-200000000000002-22-20-22-22-22-220000−i2i2−i2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000i2−i2i2−i200
χ4222-22-22-2-22002-20-2022-22-2-22-200000000000002-22-20-22-22-22-220000i2−i2i2−i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000−i2i2−i2i200
χ432-22-2-22-222002-2020-2-22-22-22-200000000000002-2-2202i−2i2i−2i−2i2i−2i2i0000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ442-22-2-22-222002-2020-2-22-22-22-200000000000002-2-2202i−2i2i−2i−2i2i−2i2i0000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ452-22-2-22-222002-2020-2-22-22-22-200000000000002-2-220−2i2i−2i2i2i−2i2i−2i0000−i2i2i2−i2000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ462-22-2-22-222002-2020-2-22-22-22-200000000000002-2-220−2i2i−2i2i2i−2i2i−2i0000i2−i2−i2i2000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ472-2-222-2-2222-200-2020-2-2222-2-22-2-220000002-220000-2−i2−i2i2i2i2i2−i2−i22-2-22000000000000000000−i2i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ482-2-222-2-2222-200-2020-2-2222-2-22-2-220000002-220000-2i2i2−i2−i2−i2−i2i2i22-2-22000000000000000000i2−i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ492-2-222-2-2222-200-2020-2-2222-2-2-222-20000002-220000-2−i2−i2i2i2i2i2−i2−i2-222-2000000000000000000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ502-2-222-2-2222-200-2020-2-2222-2-2-222-20000002-220000-2i2i2−i2−i2−i2−i2i2i2-222-2000000000000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ512-2-222-2-222-220020-20-2-2222-2-200002i−2i−2i2i00-22-200002−i2−i2i2i2i2i2−i2−i2000000002i−2i−2i2i0000000000i2−i2−i2i2−222−22−2−22000000000000
χ522-2-222-2-222-220020-20-2-2222-2-200002i−2i−2i2i00-22-200002i2i2−i2−i2−i2−i2i2i2000000002i−2i−2i2i0000000000−i2i2i2−i22−2−22−222−2000000000000
χ532-2-222-2-222-220020-20-2-2222-2-20000−2i2i2i−2i00-22-200002−i2−i2i2i2i2i2−i2−i200000000−2i2i2i−2i0000000000i2−i2−i2i22−2−22−222−2000000000000
χ542-2-222-2-222-220020-20-2-2222-2-20000−2i2i2i−2i00-22-200002i2i2−i2−i2−i2−i2i2i200000000−2i2i2i−2i0000000000−i2i2i2−i2−222−22−2−22000000000000
χ552-2-2-2222-222-2-2-222-22-2-2-2-222222-2-2-2-222-222-2-2-2-22220000000022-2-20000-2-222-2200000000000000000000000000000000
χ562-2-2-2222-222-2-2-222-22-2-2-2-2222-2-22222-2-2-222-2-2-2-222200000000-2-222000022-2-2-2200000000000000000000000000000000
χ572-2-2-2222-22-2222-2-22-2-2-2-2-222200000000-22-22222-2-2-22i2i2i2i−2i−2i−2i−2i000000000000-2200000000−2i−2i2i2i00000000000000000000
χ582-2-2-2222-22-2222-2-22-2-2-2-2-222200000000-22-22222-2-2-2−2i−2i−2i−2i2i2i2i2i000000000000-22000000002i2i−2i−2i00000000000000000000
χ592-2-2-2222-22-22-2-2-2222-2-2-2-2222000000002-2-222-2-222-2000000000000000000002-200000000000022-2-2-2-222000000000000
χ602-2-2-2222-22-22-2-2-2222-2-2-2-2222000000002-2-222-2-222-2000000000000000000002-2000000000000-2-22222-2-2000000000000
χ612-2-2-2222-2-12-2222-2-2-21111-1-1-122-2-222-2-22-2-111-1-111-100000000-1-11122-2-2-1-111-11-1-1-1-111110000000000002-2-1-111000000
χ622-2-2-2222-2-12-2222-2-2-21111-1-1-122-2-222-2-22-2-111-1-111-100000000-1-111-2-222-1-111-111111-1-1-1-1000000000000-2211-1-1000000
χ632-2-2-2222-2-12-2222-2-2-21111-1-1-1-2-222-2-2222-2-111-1-111-10000000011-1-122-2-211-1-1-11-1-1-1-11111000000000000-2211-1-1000000
χ642-2-2-2222-2-12-2222-2-2-21111-1-1-1-2-222-2-2222-2-111-1-111-10000000011-1-1-2-22211-1-1-111111-1-1-1-10000000000002-2-1-111000000
χ652-2-2-2222-2-12-2-2-222-221111-1-1-122-2-2-2-222-22-11111-1-1-100000000-1-111000011-1-11-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ662-2-2-2222-2-12-2-2-222-221111-1-1-122-2-2-2-222-22-11111-1-1-100000000-1-111000011-1-11-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ672-2-2-2222-2-12-2-2-222-221111-1-1-1-2-22222-2-2-22-11111-1-1-10000000011-1-10000-1-1111-1−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ682-2-2-2222-2-12-2-2-222-221111-1-1-1-2-22222-2-2-22-11111-1-1-10000000011-1-10000-1-1111-1i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ6944444444-2-4-444-44-44-2-2-2-2-2-2-200000000-4-4222-2-2-2-22000000000000000000002200000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200000000442222222200000000000000000000-2-200000000000000000000000000000000
χ71444-44-4-4-4-24400-40-40-2-222-2224-44-4000000-2-220000200000000-22-22000000000000000000000000000000000000000000
χ72444-44-4-4-4-24400-40-40-2-222-222-44-44000000-2-2200002000000002-22-2000000000000000000000000000000000000000000
χ73444-44-4-4-4-2-4-4004040-2-222-22200004i−4i4i−4i0022-20000-20000000000000000−2i2i−2i2i0000000000000000000000000000000000
χ74444-44-4-4-4-2-4-4004040-2-222-2220000−4i4i−4i4i0022-20000-200000000000000002i−2i2i−2i0000000000000000000000000000000000
χ7544-44-44-4-4400-44040-44-44-4-44-40000000000000-44-440000000000000000000000000000000000000000000000000000000
χ7644-44-44-4-4-2004-40-404-22-222-220000000000000-22-220000000000000−2i22i2−2i22i2000000i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ7744-44-44-4-4-2004-40-404-22-222-220000000000000-22-2200000000000002i2−2i22i2−2i2000000−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ7844-44-44-4-4-200-44040-4-22-222-2200000000000002-22-2000000000000000000000006−6−666−6−66000000000000000000000000
χ7944-44-44-4-4-200-44040-4-22-222-2200000000000002-22-200000000000000000000000−666−6−666−6000000000000000000000000
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
χ824-444-4-44-4400000000-444-4-4-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ834-444-4-44-4400000000-444-4-4-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ844-44-4-44-44400-440-404-44-44-44-40000000000000-444-40000000000000000000000000000000000000000000000000000000
χ854-44-4-44-44-2004-4040-42-22-22-220000000000000-222-20000000000000−2i22i22i2−2i2000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ864-44-4-44-44-2004-4040-42-22-22-220000000000000-222-200000000000002i2−2i2−2i22i2000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ874-44-4-44-44-200-440-4042-22-22-2200000000000002-2-22000000000000000000000006−6−66−666−6000000000000000000000000
χ884-44-4-44-44-200-440-4042-22-22-2200000000000002-2-2200000000000000000000000−666−66−6−66000000000000000000000000
χ894-4-444-4-44-24-400-404022-2-2-2224-4-44000000-22-20000200000000-222-2000000000000000000000000000000000000000000
χ904-4-444-4-44-24-400-404022-2-2-222-444-4000000-22-200002000000002-2-22000000000000000000000000000000000000000000
χ914-4-444-4-44-2-440040-4022-2-2-22200004i−4i−4i4i002-220000-20000000000000000−2i2i2i−2i0000000000000000000000000000000000
χ924-4-444-4-44-2-440040-4022-2-2-2220000−4i4i4i−4i002-220000-200000000000000002i−2i−2i2i0000000000000000000000000000000000
χ934-4-4-4444-4-2-4444-4-44-42222-2-2-200000000-442-2-2-2-2222000000000000000000002-200000000000000000000000000000000
χ944-4-4-4444-4-2-44-4-4-44442222-2-2-2000000004-42-2-222-2-2200000000000000000000-2200000000000000000000000000000000
χ9588-8-8-8-888-400000000-444-444-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-8-88-8-4000000004-4-4444-4000000000000000000000000000000000000000000000000000000000000000000000000

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