Finite Group Databasebeta

← Group #10691349

Character table — Group #10691349

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
χ91-1-1-1111-11111-11-1-1-1-1-1-1-11111-111-1-111-1-111-1-11-1-11iiii−i−i−i−i11-1-11-111-1-111-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-111-1-1ii−i−ii−i
χ101-1-1-1111-11111-11-1-1-1-1-1-1-11111-111-1-111-1-111-1-11-1-11iiii−i−i−i−i-1-1111-111-1-111-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i-11-1-111−i−iii−ii
χ111-1-1-1111-11111-11-1-1-1-1-1-1-11111-111-1-111-1-111-1-11-1-11−i−i−i−iiiii11-1-11-111-1-111-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-111-1-1−i−iii−ii
χ121-1-1-1111-11111-11-1-1-1-1-1-1-11111-111-1-111-1-111-1-11-1-11−i−i−i−iiiii-1-1111-111-1-111-1-1-1-1-1-11111−i−iii−i−i−i−iiiii-11-1-111ii−i−ii−i
χ131-1-1-1111-11111-11-1-1-1-1-1-1-11111-1-1-111-1-11111-1-11-1-11iiii−i−i−i−i11-1-11-1-1-111-1-1111111-1-1-1-1ii−i−i−i−i−i−iiiii-11-1-111ii−i−i−ii
χ141-1-1-1111-11111-11-1-1-1-1-1-1-11111-1-1-111-1-11111-1-11-1-11iiii−i−i−i−i-1-1111-1-1-111-1-111-1-1-1-11111ii−i−i−i−i−i−iiiii1-111-1-1−i−iiii−i
χ151-1-1-1111-11111-11-1-1-1-1-1-1-11111-1-1-111-1-11111-1-11-1-11−i−i−i−iiiii11-1-11-1-1-111-1-1111111-1-1-1-1−i−iiiiiii−i−i−i−i-11-1-111−i−iiii−i
χ161-1-1-1111-11111-11-1-1-1-1-1-1-11111-1-1-111-1-11111-1-11-1-11−i−i−i−iiiii-1-1111-1-1-111-1-111-1-1-1-11111−i−iiiiiii−i−i−i−i1-111-1-1ii−i−i−ii
χ1722222222222-2-2-22-222222222-2-2000000002222-2-2-2-2222222220000-2-20000000000000000-2-2-2-200000000000000000000
χ1822222222222-2-2-22-222222222-2-2000000002222-2-2-2-2-2-2-2-2-2-2-2-20000-2-20000000000000000222200000000000000000000
χ19222222222-2-2222-22-22222222-2-22222-2-2-2-2-2-2-2-22222000000000000-2-22222-2-2-2-200000000000000000000000000000000
χ20222222222-2-2222-22-22222222-2-2-2-2-2-22222-2-2-2-22222000000000000-2-2-2-2-2-2222200000000000000000000000000000000
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
χ2722222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-100000000000011-1-1-1-11111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-22222-2-2-2-21111-1-1-1-100000000000011-1-1-1-11111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000000000000111111-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1-2-2222-22-2-1-1-1-1-1-1-1-2-2-2-2-2-222221111-1-1-1-1000000000000111111-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-22-2-2-222-200020-222-2-22-2-200000000002-22-2000022-2-222-2-22−22−200000000002−22−22−22−20000000000000000002−22−200
χ32222-22-2-2-222-200020-222-2-22-2-200000000002-22-2000022-2-222-2-2−22−220000000000−22−22−22−22000000000000000000−22−2200
χ33222-22-2-2-222-200020-222-2-22-2-200000000002-22-20000-2-222-2-2222−22−200000000002−22−22−22−2000000000000000000−22−2200
χ34222-22-2-2-222-200020-222-2-22-2-200000000002-22-20000-2-222-2-222−22−220000000000−22−22−22−220000000000000000002−22−200
χ3522-22-2-22-22002-2-20202-22-2-2-22002i−2i2i−2i0000000022-2-2−i2i2−i2i2−i2i2−i2i20000002i−2i2i−2i000000000000−i2i2−i2i22−22−22−22−2000000000000
χ3622-22-2-22-22002-2-20202-22-2-2-22002i−2i2i−2i0000000022-2-2i2−i2i2−i2i2−i2i2−i20000002i−2i2i−2i000000000000i2−i2i2−i2−22−22−22−22000000000000
χ3722-22-2-22-22002-2-20202-22-2-2-2200−2i2i−2i2i0000000022-2-2−i2i2−i2i2−i2i2−i2i2000000−2i2i−2i2i000000000000−i2i2−i2i2−22−22−22−22000000000000
χ3822-22-2-22-22002-2-20202-22-2-2-2200−2i2i−2i2i0000000022-2-2i2−i2i2−i2i2−i2i2−i2000000−2i2i−2i2i000000000000i2−i2i2−i22−22−22−22−2000000000000
χ3922-22-2-22-2200-2220-202-22-2-2-220000002-22-20000-2-222−i2i2−i2i2−i2i2−i2i200000000002-22-200000000i2−i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ4022-22-2-22-2200-2220-202-22-2-2-220000002-22-20000-2-222i2−i2i2−i2i2−i2i2−i200000000002-22-200000000−i2i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ4122-22-2-22-2200-2220-202-22-2-2-22000000-22-220000-2-222−i2i2−i2i2−i2i2−i2i20000000000-22-2200000000i2−i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-22-2-22-2200-2220-202-22-2-2-22000000-22-220000-2-222i2−i2i2−i2i2−i2i2−i20000000000-22-2200000000−i2i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000
χ432-22-2-2-22220022-20-20-22-22-2-22002i−2i−2i2i000000002-22-22−22−2−22−220000002i−2i−2i2i0000000000002−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ442-22-2-2-22220022-20-20-22-22-2-22002i−2i−2i2i000000002-22-2−22−222−22−20000002i−2i−2i2i000000000000−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ452-22-2-2-22220022-20-20-22-22-2-2200−2i2i2i−2i000000002-22-22−22−2−22−22000000−2i2i2i−2i0000000000002−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ462-22-2-2-22220022-20-20-22-22-2-2200−2i2i2i−2i000000002-22-2−22−222−22−2000000−2i2i2i−2i000000000000−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ472-22-2-2-222200-2-22020-22-22-2-220000002-2-220000-22-222−22−2−22−2200000000002-2-2200000000−222−22−2−22−222−2000000000000
χ482-22-2-2-222200-2-22020-22-22-2-220000002-2-220000-22-22−22−222−22−200000000002-2-22000000002−2−22−222−22−2−22000000000000
χ492-22-2-2-222200-2-22020-22-22-2-22000000-222-20000-22-222−22−2−22−220000000000-222-200000000−222−2−222−22−2−22000000000000
χ502-22-2-2-222200-2-22020-22-22-2-22000000-222-20000-22-22−22−222−22−20000000000-222-2000000002−2−222−2−22−222−2000000000000
χ512-2-222-2-2222-2000-202-2-2222-2-200000000002-2-2200002i2i−2i−2i−2i−2i2i2i2−2−2200000000002−22−2−22−22000000000000000000i2−i2−i2i200
χ522-2-222-2-2222-2000-202-2-2222-2-200000000002-2-2200002i2i−2i−2i−2i−2i2i2i−222−20000000000−22−222−22−2000000000000000000−i2i2i2−i200
χ532-2-222-2-2222-2000-202-2-2222-2-200000000002-2-220000−2i−2i2i2i2i2i−2i−2i2−2−2200000000002−22−2−22−22000000000000000000−i2i2i2−i200
χ542-2-222-2-2222-2000-202-2-2222-2-200000000002-2-220000−2i−2i2i2i2i2i−2i−2i−222−20000000000−22−222−22−2000000000000000000i2−i2−i2i200
χ552-2-2-2222-2222-22-2-22-2-2-2-2-2222-220000000022-2-2-222-22i2i2i2i−2i−2i−2i−2i0000-220000000000000000−2i−2i2i2i00000000000000000000
χ562-2-2-2222-2222-22-2-22-2-2-2-2-2222-220000000022-2-2-222-2−2i−2i−2i−2i2i2i2i2i0000-2200000000000000002i2i−2i−2i00000000000000000000
χ572-2-2-2222-22-2-22-222-22-2-2-2-2222-2222-2-2-2-222-2-2222-2-22000000000000-2222-2-2-2-22200000000000000000000000000000000
χ582-2-2-2222-22-2-22-222-22-2-2-2-2222-22-2-22222-2-2-2-2222-2-22000000000000-22-2-22222-2-200000000000000000000000000000000
χ592-2-2-2222-22-2-2-22-2222-2-2-2-22222-200000000-2-222-222-20000000000002-20000000000000000000022-2-2-2-222000000000000
χ602-2-2-2222-22-2-2-22-2222-2-2-2-22222-200000000-2-222-222-20000000000002-200000000000000000000-2-22222-2-2000000000000
χ612-2-2-2222-2-1222-22-2-2-21111-1-1-12-222-2-222-2-2-1-111-111-10000000022-2-2-11-1-111-1-111-1-1-1-111110000000000002-2-1-111000000
χ622-2-2-2222-2-1222-22-2-2-21111-1-1-12-222-2-222-2-2-1-111-111-100000000-2-222-11-1-111-1-1111111-1-1-1-1000000000000-2211-1-1000000
χ632-2-2-2222-2-1222-22-2-2-21111-1-1-12-2-2-222-2-222-1-111-111-10000000022-2-2-1111-1-111-1-1-1-1-1-11111000000000000-2211-1-1000000
χ642-2-2-2222-2-1222-22-2-2-21111-1-1-12-2-2-222-2-222-1-111-111-100000000-2-222-1111-1-111-1-11111-1-1-1-10000000000002-2-1-111000000
χ652-2-2-2222-2-1-2-22-222-221111-1-1-1-2222-2-2-2-22211-1-1-111-10000000000001-1-1-11111-1-1−i3−i3i3i3i3i3−i3−i300000000000000−i3i3i3−i3000000
χ662-2-2-2222-2-1-2-22-222-221111-1-1-1-2222-2-2-2-22211-1-1-111-10000000000001-1-1-11111-1-1i3i3−i3−i3−i3−i3i3i300000000000000i3−i3−i3i3000000
χ672-2-2-2222-2-1-2-22-222-221111-1-1-1-22-2-22222-2-211-1-1-111-10000000000001-111-1-1-1-111−i3−i3i3i3i3i3−i3−i300000000000000i3−i3−i3i3000000
χ682-2-2-2222-2-1-2-22-222-221111-1-1-1-22-2-22222-2-211-1-1-111-10000000000001-111-1-1-1-111i3i3−i3−i3−i3−i3i3i300000000000000−i3i3i3−i3000000
χ6944444444-244-4-4-44-44-2-2-2-2-2-2-2-4-400000000-2-2-2-22222000000000000220000000000000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2440000000022222222000000000000-2-20000000000000000000000000000000000000000
χ71444-44-4-4-44-44000-40444-4-44-4-40000000000-44-440000000000000000000000000000000000000000000000000000000000
χ72444-44-4-4-4-24-400040-4-2-222-2220000000000-22-2200000000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ73444-44-4-4-4-24-400040-4-2-222-2220000000000-22-22000000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ74444-44-4-4-4-2-44000-404-2-222-22200000000002-22-200000000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ75444-44-4-4-4-2-44000-404-2-222-22200000000002-22-200000000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ7644-44-4-44-4-2004-4-4040-22-2222-2004i−4i4i−4i00000000-2-22200000000000000−2i2i−2i2i000000000000000000000000000000000000
χ7744-44-4-44-4-2004-4-4040-22-2222-200−4i4i−4i4i00000000-2-222000000000000002i−2i2i−2i000000000000000000000000000000000000
χ7844-44-4-44-4-200-4440-40-22-2222-20000004-44-4000022-2-2000000000000000000-22-2200000000000000000000000000000000
χ7944-44-4-44-4-200-4440-40-22-2222-2000000-44-44000022-2-20000000000000000002-22-200000000000000000000000000000000
χ8044-4-4-44-444000000004-4-44-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ8144-4-4-44-444000000004-4-44-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ824-444-44-4-4400000000-444-4-44-400000000000000000022−22−2222−222222−220000000000000000000000000000000000000000000000
χ834-444-44-4-4400000000-444-4-44-4000000000000000000−222222−2222−22−22220000000000000000000000000000000000000000000000
χ844-44-4-4-444-20044-40-402-22-222-2004i−4i−4i4i00000000-22-2200000000000000−2i2i2i−2i000000000000000000000000000000000000
χ854-44-4-4-444-20044-40-402-22-222-200−4i4i4i−4i00000000-22-22000000000000002i−2i−2i2i000000000000000000000000000000000000
χ864-44-4-4-444-200-4-440402-22-222-20000004-4-4400002-22-2000000000000000000-222-200000000000000000000000000000000
χ874-44-4-4-444-200-4-440402-22-222-2000000-444-400002-22-20000000000000000002-2-2200000000000000000000000000000000
χ884-4-444-4-444-4400040-4-4-4444-4-40000000000-444-40000000000000000000000000000000000000000000000000000000000
χ894-4-444-4-44-24-4000-40422-2-2-2220000000000-222-200000000000022−22−22220000000000−22−222−22−2000000000000000000000000
χ904-4-444-4-44-24-4000-40422-2-2-2220000000000-222-2000000000000−222222−2200000000002−22−2−22−22000000000000000000000000
χ914-4-444-4-44-2-4400040-422-2-2-22200000000002-2-2200000000000000000000000000i6−i6−i6i6−i6i6i6−i6000000000000000000000000
χ924-4-444-4-44-2-4400040-422-2-2-22200000000002-2-2200000000000000000000000000−i6i6i6−i6i6−i6−i6i6000000000000000000000000
χ934-4-4-4444-4-244-44-4-44-42222-2-2-2-4400000000-2-2222-2-220000000000002-20000000000000000000000000000000000000000
χ944-4-4-4444-4-2-4-4-44-44442222-2-2-24-40000000022-2-22-2-22000000000000-220000000000000000000000000000000000000000
χ9588-8-8-88-88-400000000-444-44-44000000000000000000000000000000000000000000000000000000000000000000000000
χ968-888-88-8-8-4000000004-4-444-44000000000000000000000000000000000000000000000000000000000000000000000000

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