Finite Group Databasebeta

← Group #10694455

Character table — Group #10694455

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
χ5111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
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
χ7111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
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
χ91-1-11-1-111111-1-111-1-1-1-111-1-11iiii−i−i−i−i1-11111-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i11-1-1iiii−i−i−i−i1-111-1-1ii−i−i1-1
χ101-1-11-1-111111-1-111-1-1-1-111-1-11iiii−i−i−i−i1-11111-1-1-1-11111-1-1-1-1−i−iiiiiii−i−i−i−i1-1−i−i−i−iiiii11-1-1iiii−i−i−i−i-11-1-111−i−iii-11
χ111-1-11-1-111111-1-111-1-1-1-111-1-11iiii−i−i−i−i1-11111-1-1-1-1-1-1-1-11111ii−i−iiiii−i−i−i−i1-1iiii−i−i−i−i-1-111−i−i−i−iiiii1-111-1-1−i−iii-11
χ121-1-11-1-111111-1-111-1-1-1-111-1-11iiii−i−i−i−i1-11111-1-1-1-1-1-1-1-11111−i−iiiiiii−i−i−i−i1-1−i−i−i−iiiii-1-111−i−i−i−iiiii-11-1-111ii−i−i1-1
χ131-1-11-1-111111-1-111-1-1-1-111-1-11−i−i−i−iiiii1-11111-1-1-1-11111-1-1-1-1ii−i−i−i−i−i−iiiii1-1iiii−i−i−i−i11-1-1−i−i−i−iiiii-11-1-111ii−i−i-11
χ141-1-11-1-111111-1-111-1-1-1-111-1-11−i−i−i−iiiii1-11111-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii11-1-1−i−i−i−iiiii1-111-1-1−i−iii1-1
χ151-1-11-1-111111-1-111-1-1-1-111-1-11−i−i−i−iiiii1-11111-1-1-1-1-1-1-1-11111ii−i−i−i−i−i−iiiii1-1iiii−i−i−i−i-1-111iiii−i−i−i−i-11-1-111−i−iii1-1
χ161-1-11-1-111111-1-111-1-1-1-111-1-11−i−i−i−iiiii1-11111-1-1-1-1-1-1-1-11111−i−iii−i−i−i−iiiii1-1−i−i−i−iiiii-1-111iiii−i−i−i−i1-111-1-1ii−i−i-11
χ17222222222222-2-2-2-22222222222-2-222-2-2-2-222-2-22-2-2200000000000022-2-222-2-2-2-200000000000000000000000000000000
χ18222222222222-2-2-2-222222222-2-222-2-222-2-222-2-22-2-22000000000000-2-222-2-222-2-200000000000000000000000000000000
χ19222222222-2-2-22222-2222222200000000-2-2-2-222-222-222222222000000000000-2-200000000-2-2-2-200000000000000000000
χ20222222222-2-2-22222-2222222200000000-2-2-2-222-222-2-2-2-2-2-2-2-2-2000000000000-2-200000000222200000000000000000000
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
χ2322222222-122222222-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-1000000
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
χ2522222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-100000000222211111111-1-1-1-1-1-1-1-1-1-1000000000000-2-21111000000
χ2622222222-122222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-222-1-1-1-1-1-1-1-100000000-2-2-2-211111111-1-11111111100000000000022-1-1-1-1000000
χ2722222222-1222-2-2-2-22-1-1-1-1-1-1-122-2-222-2-2-2-2-1-111-111-1000000000000-1-111-1-11111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i3000000
χ2822222222-1222-2-2-2-22-1-1-1-1-1-1-122-2-222-2-2-2-2-1-111-111-1000000000000-1-111-1-11111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i3000000
χ2922222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2-1-111-111-100000000000011-1-111-1-111−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i3000000
χ3022222222-1222-2-2-2-22-1-1-1-1-1-1-1-2-222-2-222-2-2-1-111-111-100000000000011-1-111-1-111i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i3000000
χ31222-2-2-2-222000-22-220222-2-2-2-20000000000002-202-202i2i−2i−2i2i2i−2i−2i2−22−200000000002−22−22−22−2000000000000000000−i2i2−i2i200
χ32222-2-2-2-222000-22-220222-2-2-2-20000000000002-202-202i2i−2i−2i2i2i−2i−2i−22−220000000000−22−22−22−22000000000000000000i2−i2i2−i200
χ33222-2-2-2-222000-22-220222-2-2-2-20000000000002-202-20−2i−2i2i2i−2i−2i2i2i2−22−200000000002−22−22−22−2000000000000000000i2−i2i2−i200
χ34222-2-2-2-222000-22-220222-2-2-2-20000000000002-202-20−2i−2i2i2i−2i−2i2i2i−22−220000000000−22−22−22−22000000000000000000−i2i2−i2i200
χ3522-222-2-2-222-220000-22-2-222-2-2002-2002-2002-200200-22−22−22−22−20000002-2002-200000000002−22−22−22−22−22−2000000000000
χ3622-222-2-2-222-220000-22-2-222-2-2002-2002-2002-200200-2−22−22−22−220000002-2002-20000000000−22−22−22−22−22−22000000000000
χ3722-222-2-2-222-220000-22-2-222-2-200-2200-22002-200200-22−22−22−22−2000000-2200-2200000000002−22−2−22−22−22−22000000000000
χ3822-222-2-2-222-220000-22-2-222-2-200-2200-22002-200200-2−22−22−22−22000000-2200-220000000000−22−222−22−22−22−2000000000000
χ3922-222-2-2-22-22-2000022-2-222-2-22i−2i002i−2i0000-2200-20022−22−22−22−200002i−2i002i−2i000000000000−22−22−i2i2i2−i2−i2i2i2−i2000000000000
χ4022-222-2-2-22-22-2000022-2-222-2-22i−2i002i−2i0000-2200-2002−22−22−22−2200002i−2i002i−2i0000000000002−22−2i2−i2−i2i2i2−i2−i2i2000000000000
χ4122-222-2-2-22-22-2000022-2-222-2-2−2i2i00−2i2i0000-2200-20022−22−22−22−20000−2i2i00−2i2i000000000000−22−22i2−i2−i2i2i2−i2−i2i2000000000000
χ4222-222-2-2-22-22-2000022-2-222-2-2−2i2i00−2i2i0000-2200-2002−22−22−22−220000−2i2i00−2i2i0000000000002−22−2−i2i2i2−i2−i2i2i2−i2000000000000
χ432-222-22-2-222-2-200002-22-22-22-2002i−2i00−2i2i002-200-20022−22−2−22−220000002i−2i00−2i2i00000000002−2−22i2−i2i2−i2−i2i2−i2i2000000000000
χ442-222-22-2-222-2-200002-22-22-22-2002i−2i00−2i2i002-200-2002−22−222−22−20000002i−2i00−2i2i0000000000−222−2−i2i2−i2i2i2−i2i2−i2000000000000
χ452-222-22-2-222-2-200002-22-22-22-200−2i2i002i−2i002-200-20022−22−2−22−22000000−2i2i002i−2i00000000002−2−22−i2i2−i2i2i2−i2i2−i2000000000000
χ462-222-22-2-222-2-200002-22-22-22-200−2i2i002i−2i002-200-2002−22−222−22−2000000−2i2i002i−2i0000000000−222−2i2−i2i2−i2−i2i2−i2i2000000000000
χ472-222-22-2-22-2220000-2-22-22-22-22-200-220000-2200200-22−22−2−22−2200002-200-22000000000000−222−2−222−22−2−22000000000000
χ482-222-22-2-22-2220000-2-22-22-22-22-200-220000-2200200-2−22−222−22−200002-200-220000000000002−2−222−2−22−222−2000000000000
χ492-222-22-2-22-2220000-2-22-22-22-2-22002-20000-2200200-22−22−2−22−220000-22002-2000000000000−222−22−2−22−222−2000000000000
χ502-222-22-2-22-2220000-2-22-22-22-2-22002-20000-2200200-2−22−222−22−20000-22002-20000000000002−2−22−222−22−2−22000000000000
χ512-2-22-2-222222-22-2-22-2-2-222-2-222i2i−2i−2i−2i−2i2i2i-2222-2-2-222-20000000000002i2i−2i−2i−2i−2i2i2i-2200000000000000000000000000000000
χ522-2-22-2-222222-22-2-22-2-2-222-2-22−2i−2i2i2i2i2i−2i−2i-2222-2-2-222-2000000000000−2i−2i2i2i2i2i−2i−2i-2200000000000000000000000000000000
χ532-2-22-2-2222-2-222-2-222-2-222-2-22000000002-2-2-2-2-22222000000000000000000002-200000000000022-2-2-2-222000000000000
χ542-2-22-2-2222-2-222-2-222-2-222-2-22000000002-2-2-2-2-22222000000000000000000002-2000000000000-2-22222-2-2000000000000
χ552-2-22-2-2222-2-22-222-22-2-222-2-2200000000-22-2-2222-2-222222-2-2-2-2000000000000-2200000000-2-22200000000000000000000
χ562-2-22-2-2222-2-22-222-22-2-222-2-2200000000-22-2-2222-2-22-2-2-2-22222000000000000-220000000022-2-200000000000000000000
χ572-2-22-2-222-122-22-2-22-211-1-111-12i2i−2i−2i−2i−2i2i2i-22-1-1111-1-11000000000000−i−iiiii−i−i1-133−3−3−3−33300000000000000−i3i3i3−i3000000
χ582-2-22-2-222-122-22-2-22-211-1-111-12i2i−2i−2i−2i−2i2i2i-22-1-1111-1-11000000000000−i−iiiii−i−i1-1−3−33333−3−300000000000000i3−i3−i3i3000000
χ592-2-22-2-222-122-22-2-22-211-1-111-1−2i−2i2i2i2i2i−2i−2i-22-1-1111-1-11000000000000ii−i−i−i−iii1-133−3−3−3−33300000000000000i3−i3−i3i3000000
χ602-2-22-2-222-122-22-2-22-211-1-111-1−2i−2i2i2i2i2i−2i−2i-22-1-1111-1-11000000000000ii−i−i−i−iii1-1−3−33333−3−300000000000000−i3i3i3−i3000000
χ612-2-22-2-222-122-2-222-2-211-1-111-12i2i2i2i−2i−2i−2i−2i2-2-1-1-1-11111000000002i2i−2i−2i−i−i−i−iiiii-11−i−i−i−iiiii0000000000002-2-1-111000000
χ622-2-22-2-222-122-2-222-2-211-1-111-12i2i2i2i−2i−2i−2i−2i2-2-1-1-1-1111100000000−2i−2i2i2i−i−i−i−iiiii-11iiii−i−i−i−i000000000000-2211-1-1000000
χ632-2-22-2-222-122-2-222-2-211-1-111-1−2i−2i−2i−2i2i2i2i2i2-2-1-1-1-11111000000002i2i−2i−2iiiii−i−i−i−i-11−i−i−i−iiiii000000000000-2211-1-1000000
χ642-2-22-2-222-122-2-222-2-211-1-111-1−2i−2i−2i−2i2i2i2i2i2-2-1-1-1-1111100000000−2i−2i2i2iiiii−i−i−i−i-11iiii−i−i−i−i0000000000002-2-1-111000000
χ652-2-2-222-22200022-2-20-2-22-222-20000000000002-20-2202i2i−2i−2i−2i−2i2i2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000−222−200
χ662-2-2-222-22200022-2-20-2-22-222-20000000000002-20-2202i2i−2i−2i−2i−2i2i2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i20000000000000000002−2−2200
χ672-2-2-222-22200022-2-20-2-22-222-20000000000002-20-220−2i−2i2i2i2i2i−2i−2i−i2i2i2−i20000000000−i2i2−i2i2i2−i2i2−i20000000000000000002−2−2200
χ682-2-2-222-22200022-2-20-2-22-222-20000000000002-20-220−2i−2i2i2i2i2i−2i−2ii2−i2−i2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000−222−200
χ6944444444-2-4-4-44444-4-2-2-2-2-2-2-200000000-4-422-2-22-2-22000000000000000000002200000000000000000000000000000000
χ7044444444-2-4-4-4-4-4-4-4-4-2-2-2-2-2-2-200000000442222222200000000000000000000-2-200000000000000000000000000000000
χ71444-4-4-4-4440004-44-40444-4-4-4-4000000000000-440-440000000000000000000000000000000000000000000000000000000
χ72444-4-4-4-44-20004-44-40-2-2-222220000000000002-202-200000000000000000000000i6−i6−i6i6i6−i6−i6i6000000000000000000000000
χ73444-4-4-4-44-20004-44-40-2-2-222220000000000002-202-200000000000000000000000−i6i6i6−i6−i6i6i6−i6000000000000000000000000
χ74444-4-4-4-44-2000-44-440-2-2-22222000000000000-220-2200000000022−2222−220000000000−22−22−22−22000000000000000000000000
χ75444-4-4-4-44-2000-44-440-2-2-22222000000000000-220-22000000000−2222−222200000000002−22−22−22−2000000000000000000000000
χ7644-444-4-4-4-24-440000-4-222-2-222004-4004-400-2200-200200000000000000-2200-220000000000000000000000000000000000
χ7744-444-4-4-4-24-440000-4-222-2-22200-4400-4400-2200-2002000000000000002-2002-20000000000000000000000000000000000
χ7844-444-4-4-4-2-44-400004-222-2-2224i−4i004i−4i00002-200200-2000000000000−2i2i00−2i2i000000000000000000000000000000000000
χ7944-444-4-4-4-2-44-400004-222-2-222−4i4i00−4i4i00002-200200-20000000000002i−2i002i−2i000000000000000000000000000000000000
χ8044-4-4-444-44000000004-4-4-4-444000000000000000000−2i22i22i2−2i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ8144-4-4-444-44000000004-4-4-4-4440000000000000000002i2−2i2−2i22i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ824-444-44-4-4-24-4-4000042-22-22-22004i−4i00−4i4i00-2200200-200000000000000−2i2i002i−2i0000000000000000000000000000000000
χ834-444-44-4-4-24-4-4000042-22-22-2200−4i4i004i−4i00-2200200-2000000000000002i−2i00−2i2i0000000000000000000000000000000000
χ844-444-44-4-4-2-4440000-42-22-22-224-400-4400002-200-2002000000000000-22002-2000000000000000000000000000000000000
χ854-444-44-4-4-2-4440000-42-22-22-22-44004-400002-200-20020000000000002-200-22000000000000000000000000000000000000
χ864-44-44-44-4400000000-44-4-44-44000000000000000000−2i22i22i2−2i22i2−2i2−2i22i20000000000000000000000000000000000000000000000
χ874-44-44-44-4400000000-44-4-44-440000000000000000002i2−2i2−2i22i2−2i22i22i2−2i20000000000000000000000000000000000000000000000
χ884-4-44-4-444-2-4-444-4-44422-2-222-2000000004-42222-2-2-2-200000000000000000000-2200000000000000000000000000000000
χ894-4-44-4-444-2-4-44-444-4422-2-222-200000000-4422-2-2-222-2000000000000000000002-200000000000000000000000000000000
χ904-4-4-444-444000-4-4440-4-44-444-4000000000000-4404-40000000000000000000000000000000000000000000000000000000
χ914-4-4-444-44-200044-4-4022-22-2-22000000000000-2202-2000000000−2i22i22i2−2i20000000000i2−i2i2−i2−i2i2−i2i2000000000000000000000000
χ924-4-4-444-44-200044-4-4022-22-2-22000000000000-2202-20000000002i2−2i2−2i22i20000000000−i2i2−i2i2i2−i2i2−i2000000000000000000000000
χ934-4-4-444-44-2000-4-444022-22-2-220000000000002-20-22000000000000000000000006−6−66−666−6000000000000000000000000
χ944-4-4-444-44-2000-4-444022-22-2-220000000000002-20-2200000000000000000000000−666−66−6−66000000000000000000000000
χ9588-8-8-888-8-400000000-44444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ968-88-88-88-8-4000000004-444-44-4000000000000000000000000000000000000000000000000000000000000000000000000

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