Finite Group Databasebeta

← Group #10694976

Character table — Group #10694976

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111222222222222222222224444444444444444444444444444444444441212121212121212121212121212121216161616161616161616161648484848
order122222223444444444444666666688888888121212121212121212121212242424242424242424242424242424248888888888888888444412121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1
χ91-1-11-11-111-1-11111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−ii−i1-1ii−i−i11-1-1i−i1-1
χ101-1-11-11-111-1-11111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i−ii-11−i−iii-1-111−ii-11
χ111-1-11-11-111-1-11111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiiii−i1-1ii−i−i11-1-1−ii-11
χ121-1-11-11-111-1-11111-1-111-1-1-1-1-111-11iiii−i−i−i−i1111-1-111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii−ii-11−i−iii-1-111i−i1-1
χ131-1-11-11-111-1-11111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiiii−i-11ii−i−i-1-111i−i-11
χ141-1-11-11-111-1-11111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii−ii1-1−i−iii11-1-1−ii1-1
χ151-1-11-11-111-1-11111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−ii−i-11ii−i−i-1-111−ii1-1
χ161-1-11-11-111-1-11111-1-111-1-1-1-1-111-11−i−i−i−iiiii1111-1-111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i−ii1-1−i−iii11-1-1i−i-11
χ1722222222222-2-2-2-2-2-222-2-222222220000000022-2-222-2-2-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ1822222222222-2-2-2-2-2-222-2-222222220000000022-2-222-2-2-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ19222222222-2-222-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-200000000000000000000000022-2-222-2-20000000000000000
χ20222222222-2-222-2-2-2-2-2-222222222200000000-2-2-2-2-2-22222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ21222222222-2-2-2-22222-2-2-2-2222222222-2-222-2-2-2-222-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ22222222222-2-2-2-22222-2-2-2-22222222-2-222-2-222-2-222-2-2-2-2-2-222-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2322222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-10000
χ2422222222-1222222222222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2-2111111110000
χ2522222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111111111111000000000000000022-2-2-1-1-1-111110000
χ2622222222-1222222222222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000-2-2221111-1-1-1-10000
χ2722222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211-1-1111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000−i3i3−i3i3−i3i3−i3i30000
χ2822222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-122-2-222-2-211-1-1111111-1-1-1-1-1-11111-1-1-1-1111100000000000000000000i3−i3i3−i3i3−i3i3−i30000
χ2922222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211-1-1111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000−i3i3−i3i3i3−i3i3−i30000
χ3022222222-1-2-2-2-22222-2-2-2-2-1-1-1-1-1-1-1-2-222-2-22211-1-1111111-1-11111-1-1-1-11111-1-1-1-100000000000000000000i3−i3i3−i3−i3i3−i3i30000
χ3122-2-222-2-22002-20000002-22-2-2-2-2222−22−22−22−20000002-22-20022−2−222−2−222−2−222−2−2−i2i2−i2i2−i2i2−i2i2002i−2i002i−2i0000000000000000
χ3222-2-222-2-22002-20000002-22-2-2-2-2222−22−22−22−20000002-22-20022−2−222−2−222−2−222−2−2i2−i2i2−i2i2−i2i2−i200−2i2i00−2i2i0000000000000000
χ3322-2-222-2-22002-20000002-22-2-2-2-222−22−22−22−220000002-22-200−2−222−2−222−2−222−2−222−i2i2−i2i2−i2i2−i2i200−2i2i00−2i2i0000000000000000
χ3422-2-222-2-22002-20000002-22-2-2-2-222−22−22−22−220000002-22-200−2−222−2−222−2−222−2−222i2−i2i2−i2i2−i2i2−i2002i−2i002i−2i0000000000000000
χ3522-2-222-2-2200-22000000-222-2-2-2-2222−2−222−2−22000000-22-220022−2−2−2−22222−2−2−2−222−i2i2i2−i2−i2i2i2−i22i−2i002i−2i000000000000000000
χ3622-2-222-2-2200-22000000-222-2-2-2-2222−2−222−2−22000000-22-220022−2−2−2−22222−2−2−2−222i2−i2−i2i2i2−i2−i2i2−2i2i00−2i2i000000000000000000
χ3722-2-222-2-2200-22000000-222-2-2-2-222−222−2−222−2000000-22-2200−2−22222−2−2−2−22222−2−2−i2i2i2−i2−i2i2i2−i2−2i2i00−2i2i000000000000000000
χ3822-2-222-2-2200-22000000-222-2-2-2-222−222−2−222−2000000-22-2200−2−22222−2−2−2−22222−2−2i2−i2−i2i2i2−i2−i2i22i−2i002i−2i000000000000000000
χ392-22-2-222-22002-2000000-22-222-2-2-22−i2i2−i2i2i2−i2i2−i20000002-2-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2i2−i2i2i2−i2i2−i2002-200-220000000000000000
χ402-22-2-222-22002-2000000-22-222-2-2-22−i2i2−i2i2i2−i2i2−i20000002-2-2200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2i2−i2i2−i2−i2i2−i2i200-22002-20000000000000000
χ412-22-2-222-22002-2000000-22-222-2-2-22i2−i2i2−i2−i2i2−i2i20000002-2-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−i2i2−i2i2i2−i2i2−i200-22002-20000000000000000
χ422-22-2-222-22002-2000000-22-222-2-2-22i2−i2i2−i2−i2i2−i2i20000002-2-2200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2−i2i2−i2−i2i2−i2i2002-200-220000000000000000
χ432-22-2-222-2200-220000002-2-222-2-2-22−i2i2i2−i2i2−i2−i2i2000000-222-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2i2i2−i2i2−i2−i2i22-200-22000000000000000000
χ442-22-2-222-2200-220000002-2-222-2-2-22−i2i2i2−i2i2−i2−i2i2000000-222-200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2−i2−i2i2−i2i2i2−i2-22002-2000000000000000000
χ452-22-2-222-2200-220000002-2-222-2-2-22i2−i2−i2i2−i2i2i2−i2000000-222-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2i2i2−i2i2−i2−i2i2-22002-2000000000000000000
χ462-22-2-222-2200-220000002-2-222-2-2-22i2−i2−i2i2−i2i2i2−i2000000-222-200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2−i2−i2i2−i2i2i2−i22-200-22000000000000000000
χ472-2-22-22-2222222-2-222-2-2-2-2-2-2-222-2200000000-2-2-2-22222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ482-2-22-22-2222222-2-222-2-2-2-2-2-2-222-2200000000-2-2-2-22222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ492-2-22-22-22222-2-222-2-2-2-222-2-2-222-222i2i−2i−2i−2i−2i2i2i-2-22222-2-222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ502-2-22-22-22222-2-222-2-2-2-222-2-2-222-22−2i−2i2i2i2i2i−2i−2i-2-22222-2-222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ512-2-22-22-222-2-2-2-2-2-2222222-2-2-222-220000000022-2-2-2-2-2-22222000000000000000022-2-2-2-222000000000000000000000000
χ522-2-22-22-222-2-2-2-2-2-2222222-2-2-222-220000000022-2-2-2-2-2-222220000000000000000-2-22222-2-2000000000000000000000000
χ532-2-22-22-22-122-2-222-2-2-2-222111-1-11-12i2i−2i−2i−2i−2i2i2i11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i000000000000000000003−3−33−i3i3i3−i30000
χ542-2-22-22-22-122-2-222-2-2-2-222111-1-11-12i2i−2i−2i−2i−2i2i2i11-1-1-1-111-1-111−i−i−i−iiiiiiiii−i−i−i−i00000000000000000000−333−3i3−i3−i3i30000
χ552-2-22-22-22-122-2-222-2-2-2-222111-1-11-1−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii000000000000000000003−3−33i3−i3−i3i30000
χ562-2-22-22-22-122-2-222-2-2-2-222111-1-11-1−2i−2i2i2i2i2i−2i−2i11-1-1-1-111-1-111iiii−i−i−i−i−i−i−i−iiiii00000000000000000000−333−3−i3i3i3−i30000
χ572-2-22-22-22-1-2-22222-2-222-2-2111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii00000000000000002i−2i2-2−i−iii-1-1110000
χ582-2-22-22-22-1-2-22222-2-222-2-2111-1-11-12i2i2i2i−2i−2i−2i−2i-1-1-1-111-1-11111−i−i−i−i−i−i−i−iiiiiiiii0000000000000000−2i2i-22ii−i−i11-1-10000
χ592-2-22-22-22-1-2-22222-2-222-2-2111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i00000000000000002i−2i-22−i−iii11-1-10000
χ602-2-22-22-22-1-2-22222-2-222-2-2111-1-11-1−2i−2i−2i−2i2i2i2i2i-1-1-1-111-1-11111iiiiiiii−i−i−i−i−i−i−i−i0000000000000000−2i2i2-2ii−i−i-1-1110000
χ6144444444-244-4-4-4-4-4-444-4-4-2-2-2-2-2-2-200000000-2-222-2-2222222000000000000000000000000000000000000000000000000
χ6244444444-2-4-444-4-4-4-4-4-444-2-2-2-2-2-2-200000000222222-2-2-2-222000000000000000000000000000000000000000000000000
χ63444-4-4-4-44400004-44-4000044-44-4-4-400000000004-40000004-4000000000000000000000000000000000000000000000000
χ64444-4-4-4-4440000-44-44000044-44-4-4-40000000000-44000000-44000000000000000000000000000000000000000000000000
χ65444-4-4-4-44-200004-44-40000-2-22-22220000000000-22000000-22−2i32i3−2i32i30000−2i32i3−2i32i3000000000000000000000000000000000000
χ66444-4-4-4-44-200004-44-40000-2-22-22220000000000-22000000-222i3−2i32i3−2i300002i3−2i32i3−2i3000000000000000000000000000000000000
χ67444-4-4-4-44-20000-44-440000-2-22-222200000000002-20000002-20000−2i32i3−2i32i30000−2i32i3−2i32i300000000000000000000000000000000
χ68444-4-4-4-44-20000-44-440000-2-22-222200000000002-20000002-200002i3−2i32i3−2i300002i3−2i32i3−2i300000000000000000000000000000000
χ6944-44-4-44-444-40000004-4004-44-44-4-4000000004-4004-4000000000000000000000000000000000000000000000000000000
χ7044-44-4-44-44-44000000-44004-44-44-4-400000000-4400-44000000000000000000000000000000000000000000000000000000
χ7144-44-4-44-4-24-40000004-400-22-22-22200000000-2200-22000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i600000000000000000000000000000000
χ7244-44-4-44-4-24-40000004-400-22-22-22200000000-2200-22000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i6−i6i6i6−i600000000000000000000000000000000
χ7344-44-4-44-4-2-44000000-4400-22-22-222000000002-2002-2000000i6−i6−i6i6−i6i6i6−i6i6−i6−i6i6−i6i6i6−i600000000000000000000000000000000
χ7444-44-4-44-4-2-44000000-4400-22-22-222000000002-2002-2000000−i6i6i6−i6i6−i6−i6i6−i6i6i6−i6i6−i6−i6i600000000000000000000000000000000
χ7544-4-444-4-4-2004-40000004-4-22222-2-222−2222−2222−2222−22000000-22-2200−2−222−2−222−2−222−2−22200000000000000000000000000000000
χ7644-4-444-4-4-2004-40000004-4-22222-2-2−2222−2222−2222−2222000000-22-220022−2−222−2−222−2−222−2−200000000000000000000000000000000
χ7744-4-444-4-4-200-44000000-44-22222-2-222−22−222222−22−22220000002-22-200−2−22222−2−2−2−22222−2−200000000000000000000000000000000
χ7844-4-444-4-4-200-44000000-44-22222-2-2−222222−22−222222−220000002-22-20022−2−2−2−22222−2−2−2−22200000000000000000000000000000000
χ794-4444-4-4-444-4000000-4400-44-4-444-400000000-44004-4000000000000000000000000000000000000000000000000000000
χ804-4444-4-4-44-440000004-400-44-4-444-4000000004-400-44000000000000000000000000000000000000000000000000000000
χ814-4444-4-4-4-24-4000000-44002-222-2-22000000002-200-220000006−6−66−666−6−666−66−6−6600000000000000000000000000000000
χ824-4444-4-4-4-24-4000000-44002-222-2-22000000002-200-22000000−666−66−6−666−6−66−666−600000000000000000000000000000000
χ834-4444-4-4-4-2-440000004-4002-222-2-2200000000-22002-20000006−6−666−6−66−666−6−666−600000000000000000000000000000000
χ844-4444-4-4-4-2-440000004-4002-222-2-2200000000-22002-2000000−666−6−666−66−6−666−6−6600000000000000000000000000000000
χ854-44-4-444-4-2004-4000000-442-2-2222-2−2i22i2−2i22i22i2−2i22i2−2i2000000-222-200i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000000000000000000000000000
χ864-44-4-444-4-2004-4000000-442-2-2222-22i2−2i22i2−2i2−2i22i2−2i22i2000000-222-200−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000000000000000000000000000
χ874-44-4-444-4-200-440000004-42-2-2222-2−2i22i22i2−2i22i2−2i2−2i22i20000002-2-2200i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000000000000000000000000000
χ884-44-4-444-4-200-440000004-42-2-2222-22i2−2i2−2i22i2−2i22i22i2−2i20000002-2-2200−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000000000000000000000000000
χ894-4-44-44-44-24444-4-444-4-4-4-4222-2-22-2000000002222-2-2-2-222-2-2000000000000000000000000000000000000000000000000
χ904-4-44-44-44-2-4-4-4-4-4-4444444222-2-22-200000000-2-2222222-2-2-2-2000000000000000000000000000000000000000000000000
χ914-4-4-44-444400004-4-440000-4-444-44-400000000004-4000000-44000000000000000000000000000000000000000000000000
χ924-4-4-44-44440000-444-40000-4-444-44-40000000000-440000004-4000000000000000000000000000000000000000000000000
χ934-4-4-44-444-200004-4-44000022-2-22-220000000000-220000002-223−2323−230000−2323−2323000000000000000000000000000000000000
χ944-4-4-44-444-200004-4-44000022-2-22-220000000000-220000002-2−2323−2323000023−2323−23000000000000000000000000000000000000
χ954-4-4-44-444-20000-444-4000022-2-22-2200000000002-2000000-22000023−2323−230000−2323−232300000000000000000000000000000000
χ964-4-4-44-444-20000-444-4000022-2-22-2200000000002-2000000-220000−2323−2323000023−2323−2300000000000000000000000000000000

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