Finite Group Databasebeta

← Group #10840190

Character table — Group #10840190

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size11111111222222222222444444444444448888888888888888888888888881212121212121616161616242424242424242424242448
order12222222344446666666224444666612121212444448888121212121212121212122424242424242424224444412121212444444488884
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-111-1-1-1-1-1
χ411111111111111111111111111111111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-11
χ61111111111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-1111111-1
χ71111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-11-1-1-1-1-1-11111-1
χ81111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ911111111111111111111-1-11111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1111-1-1-1-111-1-1111
χ1011111111111111111111-1-11111-1-1-1-11111-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-111-11111-1-111-1-1-1
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11-1-1111111-1-1-1
χ1211111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-11111111-1-1-111-1-1-1-1-1-1111
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111111-1-1-1-111-1-11
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-11111-11111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-111-1-1-11111-1-111-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1111-1-111111-1-1-1-111-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-11111-1-11
χ17222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-2000000000000000022-2-22200000-200000000000
χ18222222222-2-2-2-222222222200002222-2-2-2-2-200000000-2-20000000000000000-2-222-2-200000200000000000
χ19222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-22000000002200000000000000002222-2-200000-200000000000
χ20222222222-2-2-2-22222222-2-20000-2-2-2-2-2-2-2-2200000000220000000000000000-2-2-2-22200000200000000000
χ2122222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000002-1-1-1-1000000000000
χ2222222222-12222-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-12-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-111111111000000-21111000000000000
χ2322222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1222-2-2-2-2-2-2-1-111111111111111110000002-1-1-1-1000000000000
χ2422222222-12222-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-12-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000-21111000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-222-2-222-2-211-1-1-1-11111-1-1-1-11111000000-211-1-1000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-222221111-1-1-1-1-2-2-2-2-2-2-22211-1-1-1-111111111-1-1-1-10000002-1-111000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-22222-2-222111111-1-1-1-11111-1-1-1-1000000-211-1-1000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-21111-1-1-1-1-2-2-22222-2-2111111-1-1-1-1-1-1-1-111110000002-1-111000000000000
χ2922-2-22-2-22222-2-22-2-2-2-2220022-2-200002-22-20000000000022-2-2000000000000000000000000002i−2i002i−2i000
χ3022-2-22-2-22222-2-22-2-2-2-2220022-2-200002-22-20000000000022-2-200000000000000000000000000−2i2i00−2i2i000
χ3122-2-22-2-22222-2-22-2-2-2-22200-2-22200002-22-200000000000-2-222000000000000000000000000002i−2i00−2i2i000
χ3222-2-22-2-22222-2-22-2-2-2-22200-2-22200002-22-200000000000-2-22200000000000000000000000000−2i2i002i−2i000
χ332-22-22-22-222-2-22-222-2-22-2002i−2i2i−2i00002-2-22000000000002i−2i2i−2i000000000000002-22-20000002i−2i000000000
χ342-22-22-22-222-2-22-222-2-22-2002i−2i2i−2i00002-2-22000000000002i−2i2i−2i00000000000000-22-22000000−2i2i000000000
χ352-22-22-22-222-2-22-222-2-22-200−2i2i−2i2i00002-2-2200000000000−2i2i−2i2i000000000000002-22-2000000−2i2i000000000
χ362-22-22-22-222-2-22-222-2-22-200−2i2i−2i2i00002-2-2200000000000−2i2i−2i2i00000000000000-22-220000002i−2i000000000
χ372-22-22-22-22-222-2-222-2-22-20000000000-222-20002i−2i00000000002i2i−2i−2i00000000002-2-2200000000002i−2i00000
χ382-22-22-22-22-222-2-222-2-22-20000000000-222-20002i−2i00000000002i2i−2i−2i0000000000-222-20000000000−2i2i00000
χ392-22-22-22-22-222-2-222-2-22-20000000000-222-2000−2i2i0000000000−2i−2i2i2i00000000002-2-220000000000−2i2i00000
χ402-22-22-22-22-222-2-222-2-22-20000000000-222-2000−2i2i0000000000−2i−2i2i2i0000000000-222-200000000002i−2i00000
χ412-2-2222-2-222-22-2-2-2-2222-2002i−2i−2i2i000022-2-202-2002i−2i00002i−2i−2i2i00002i2i−2i−2i00000000000002-2000000000000
χ422-2-2222-2-222-22-2-2-2-2222-2002i−2i−2i2i000022-2-20-2200−2i2i00002i−2i−2i2i0000−2i−2i2i2i0000000000000-22000000000000
χ432-2-2222-2-222-22-2-2-2-2222-200−2i2i2i−2i000022-2-202-200−2i2i0000−2i2i2i−2i0000−2i−2i2i2i00000000000002-2000000000000
χ442-2-2222-2-222-22-2-2-2-2222-200−2i2i2i−2i000022-2-20-22002i−2i0000−2i2i2i−2i00002i2i−2i−2i0000000000000-22000000000000
χ452-2-2222-2-2-12-22-2111-1-1-11002i−2i−2i2i−i3−i3i3i3-1-11102-2002i−2i00−i3i3−iii−i3−33−3−i−iii33−3−30000000−i3i3-11000000000000
χ462-2-2222-2-2-12-22-2111-1-1-11002i−2i−2i2i−i3−i3i3i3-1-1110-2200−2i2i00−i3i3−iii−i3−33−3ii−i−i−3−3330000000i3−i31-1000000000000
χ472-2-2222-2-2-12-22-2111-1-1-11002i−2i−2i2ii3i3−i3−i3-1-11102-2002i−2i00i3−i3−iii−i−33−33−i−iii−3−3330000000i3−i3-11000000000000
χ482-2-2222-2-2-12-22-2111-1-1-11002i−2i−2i2ii3i3−i3−i3-1-1110-2200−2i2i00i3−i3−iii−i−33−33ii−i−i33−3−30000000−i3i31-1000000000000
χ492-2-2222-2-2-12-22-2111-1-1-1100−2i2i2i−2i−i3−i3i3i3-1-11102-200−2i2i00−i3i3i−i−ii−33−33ii−i−i−3−3330000000−i3i3-11000000000000
χ502-2-2222-2-2-12-22-2111-1-1-1100−2i2i2i−2i−i3−i3i3i3-1-1110-22002i−2i00−i3i3i−i−ii−33−33−i−iii33−3−30000000i3−i31-1000000000000
χ512-2-2222-2-2-12-22-2111-1-1-1100−2i2i2i−2ii3i3−i3−i3-1-11102-200−2i2i00i3−i3i−i−ii3−33−3ii−i−i33−3−30000000i3−i3-11000000000000
χ522-2-2222-2-2-12-22-2111-1-1-1100−2i2i2i−2ii3i3−i3−i3-1-1110-22002i−2i00i3−i3i−i−ii3−33−3−i−iii−3−3330000000−i3i31-1000000000000
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-2440000-2-2-2-22222-40000000022000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4000022222222400000000-2-2000000000000000000000000000000000000000
χ55444-4-44-4-44000044-4-44-4-4000000000000000000000000000000000000000000000000000000000000022−220
χ56444-4-44-4-44000044-4-44-4-40000000000000000000000000000000000000000000000000000000000000−22220
χ5744-44-4-44-4400004-444-4-4-44-400004-44-4000000000000000000000000000000000000000000000000000000
χ5844-44-4-44-4400004-444-4-4-4-440000-44-44000000000000000000000000000000000000000000000000000000
χ5944-44-4-44-4-20000-22-2-22224-40000-22-2200000000000000000000000i6−i6i6−i6i6−i6i6−i600000000000000000000000
χ6044-44-4-44-4-20000-22-2-22224-40000-22-2200000000000000000000000−i6i6−i6i6−i6i6−i6i600000000000000000000000
χ6144-44-4-44-4-20000-22-2-2222-4400002-22-200000000000000000000000i6−i6i6−i6−i6i6−i6i600000000000000000000000
χ6244-44-4-44-4-20000-22-2-2222-4400002-22-200000000000000000000000−i6i6−i6i6i6−i6i6−i600000000000000000000000
χ6344-4-44-4-444-4-4444-4-4-4-4440000000000-44-4400000000000000000000000000000000000000000000000000
χ6444-4-44-4-44-244-4-4-22222-2-20044-4-40000-22-2200000000000-2-22200000000000000000000000000000000000
χ6544-4-44-4-44-244-4-4-22222-2-200-4-4440000-22-220000000000022-2-200000000000000000000000000000000000
χ6644-4-44-4-44-2-4-444-22222-2-200000000002-22-2000000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6744-4-44-4-44-2-4-444-22222-2-200000000002-22-20000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ684-444-4-4-4440000-44-44-4-44000000000000000000000−2i22i200000000000000−2i22i22i2−2i200000000000000000000000
χ694-444-4-4-4440000-44-44-4-440000000000000000000002i2−2i2000000000000002i2−2i2−2i22i200000000000000000000000
χ704-444-4-4-44-200002-22-222-2000000−2i32i32i3−2i300000000000−2i22i20000000000−666−6i2−i2−i2i200000000000000000000000
χ714-444-4-4-44-200002-22-222-2000000−2i32i32i3−2i3000000000002i2−2i200000000006−6−66−i2i2i2−i200000000000000000000000
χ724-444-4-4-44-200002-22-222-20000002i3−2i3−2i32i300000000000−2i22i200000000006−6−66i2−i2−i2i200000000000000000000000
χ734-444-4-4-44-200002-22-222-20000002i3−2i3−2i32i3000000000002i2−2i20000000000−666−6−i2i2i2−i200000000000000000000000
χ744-44-44-44-4-24-4-442-2-222-22004i−4i4i−4i0000-222-200000000000−2i2i−2i2i00000000000000000000000000000000000
χ754-44-44-44-4-24-4-442-2-222-2200−4i4i−4i4i0000-222-2000000000002i−2i2i−2i00000000000000000000000000000000000
χ764-44-44-44-4-2-444-42-2-222-2200000000002-2-220004i−4i0000000000−2i−2i2i2i0000000000000000000000000000000
χ774-44-44-44-4-2-444-42-2-222-2200000000002-2-22000−4i4i00000000002i2i−2i−2i0000000000000000000000000000000
χ784-4-4444-4-44-44-44-4-4-4444-40000000000-4-44400000000000000000000000000000000000000000000000000
χ794-4-4444-4-4-2-44-44222-2-2-22000000−2i3−2i32i32i322-2-20000000002i3−2i3000000000000000000000000000000000000000
χ804-4-4444-4-4-2-44-44222-2-2-220000002i32i3−2i3−2i322-2-2000000000−2i32i3000000000000000000000000000000000000000
χ814-4-4-4-444440000-4-44-44-44000000000000000000000000000000000000000004-4000000000000000000000
χ824-4-4-4-444440000-4-44-44-4400000000000000000000000000000000000000000-44000000000000000000000
χ83888-8-88-8-8-40000-4-444-4440000000000000000000000000000000000000000000000000000000000000000
χ848-8-8-8-8888-4000044-44-44-40000000000000000000000000000000000000000000000000000000000000000

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