Finite Group Databasebeta

← Group #10840247

Character table — Group #10840247

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111111112222222222224444444444444444888888888888888888888888121212121616161616162424242424242424242424242424
order122222223444466666664444444412121212121212124488881212121212121212121224242424242424242244441212121224444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1111-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11-1-1-1-1-1-11-1-11111
χ6111111111111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111111-111-1-1-1-1
χ7111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-1111-1-1-1-1
χ8111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-111-1-1-11111
χ911111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-11-111-1-1-1-1-111111-1-111-1-1
χ1011111111111111111111-1-1-1-11111111-1-1-1-11-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111-111-1-1111-1-1-1-1-111-1-111
χ1111111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1-11-1-111-1-1-1-1-111111-1-111
χ1211111111111111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111-11-1-11111111-1-1-1-1-111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-111-111-1-1-1-111111-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-1111-1-11111-1-1-1-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-111-1-1-11111-1-11-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1111-111-1-11-1-1-1-111-11111-1-1
χ17222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-200000022000000000000000022-2-20000002000000-2000000
χ18222222222-2-2-2-2222222222-2-20000-2-2-2-2-2-2-2-2000000220000000000000000-2-222000000-20000002000000
χ19222222222-2-2-2-22222222-2-2220000-2-2-22222-2000000-2-200000000000000002222000000-2000000-2000000
χ20222222222-2-2-2-22222222-2-2220000-2-2-22222-2000000-2-20000000000000000-2-2-2-200000020000002000000
χ2122222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-100000000000000
χ2222222222-12222-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-1-1111111110000-2-2111100000000000000
χ2322222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-22222-1-111111111-1-1-1-1-1-1-1-10000-2-2111100000000000000
χ2422222222-12222-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-2-1-11111111111111111000022-1-1-1-100000000000000
χ2522222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-222-2-211-1-1-1-11111-1-1-1-1111100002-2-1-11100000000000000
χ2622222222-12222-1-1-1-1-1-1-1-2-2-2-22222-1-1-11111-1-2-2-2-22211-1-1-1-111111111-1-1-1-10000-2211-1-100000000000000
χ2722222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-12222-2-2111111-1-1-1-1-1-1-1-111110000-2211-1-100000000000000
χ2822222222-12222-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111-122-2-222111111-1-1-1-11111-1-1-1-100002-2-1-11100000000000000
χ2922-2-2-22-22222-2-2-2222-2-2-22-22-22i2i−2i−2i2-2-222-2-222i−2i00002-22i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000
χ3022-2-2-22-22222-2-2-2222-2-2-22-22-2−2i−2i2i2i2-2-222-2-22−2i2i00002-2−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000
χ3122-2-2-22-22222-2-2-2222-2-2-2-22-222i2i−2i−2i2-2-2-2-2222−2i2i0000-222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ3222-2-2-22-22222-2-2-2222-2-2-2-22-22−2i−2i2i2i2-2-2-2-22222i−2i0000-22−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ3322-2-2-22-222-2-222-2222-2-2-22-2-220000-222-2-222-20000002-20000000000000000000000000002i−2i002i−2i0000000
χ3422-2-2-22-222-2-222-2222-2-2-22-2-220000-222-2-222-20000002-2000000000000000000000000000−2i2i00−2i2i0000000
χ3522-2-2-22-222-2-222-2222-2-2-2-222-20000-22222-2-2-2000000-220000000000000000000000000002i−2i00−2i2i0000000
χ3622-2-2-22-222-2-222-2222-2-2-2-222-20000-22222-2-2-2000000-22000000000000000000000000000−2i2i002i−2i0000000
χ3722-2-2-22-22-122-2-21-1-1-11112-22-22i2i−2i−2i-111-1-111-12i−2i0000-11−i−iii−i−iii−i3−i3i3i3−i3−i3i3i30000003−33−300000000000000
χ3822-2-2-22-22-122-2-21-1-1-11112-22-22i2i−2i−2i-111-1-111-12i−2i0000-11−i−iii−i−iiii3i3−i3−i3i3i3−i3−i3000000−33−3300000000000000
χ3922-2-2-22-22-122-2-21-1-1-11112-22-2−2i−2i2i2i-111-1-111-1−2i2i0000-11ii−i−iii−i−i−i3−i3i3i3−i3−i3i3i3000000−33−3300000000000000
χ4022-2-2-22-22-122-2-21-1-1-11112-22-2−2i−2i2i2i-111-1-111-1−2i2i0000-11ii−i−iii−i−ii3i3−i3−i3i3i3−i3−i30000003−33−300000000000000
χ4122-2-2-22-22-122-2-21-1-1-1111-22-222i2i−2i−2i-11111-1-1-1−2i2i00001-1−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i30000003−3−3300000000000000
χ4222-2-2-22-22-122-2-21-1-1-1111-22-222i2i−2i−2i-11111-1-1-1−2i2i00001-1−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3000000−333−300000000000000
χ4322-2-2-22-22-122-2-21-1-1-1111-22-22−2i−2i2i2i-11111-1-1-12i−2i00001-1ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3000000−333−300000000000000
χ4422-2-2-22-22-122-2-21-1-1-1111-22-22−2i−2i2i2i-11111-1-1-12i−2i00001-1ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i30000003−3−3300000000000000
χ452-222-2-2-2222-22-2-22-2-22-2200002i−2i2i−2i22-20000-2000000002i−2i2i−2i0000000000000000000000000000002-2002i−2i
χ462-222-2-2-2222-22-2-22-2-22-2200002i−2i2i−2i22-20000-2000000002i−2i2i−2i000000000000000000000000000000-2200−2i2i
χ472-222-2-2-2222-22-2-22-2-22-220000−2i2i−2i2i22-20000-200000000−2i2i−2i2i0000000000000000000000000000002-200−2i2i
χ482-222-2-2-2222-22-2-22-2-22-220000−2i2i−2i2i22-20000-200000000−2i2i−2i2i000000000000000000000000000000-22002i−2i
χ492-2-2-22-22222-2-2222-2-2-22-200002-2-222-220000-2000000002-2-2200000000000000000000000002i−2i000002i−2i00
χ502-2-2-22-22222-2-2222-2-2-22-200002-2-222-220000-2000000002-2-220000000000000000000000000−2i2i00000−2i2i00
χ512-2-2-22-22222-2-2222-2-2-22-20000-222-22-220000-200000000-222-200000000000000000000000002i−2i00000−2i2i00
χ522-2-2-22-22222-2-2222-2-2-22-20000-222-22-220000-200000000-222-20000000000000000000000000−2i2i000002i−2i00
χ5344444444-2-4-4-4-4-2-2-2-2-2-2-244-4-4000022222222000000-2-20000000000000000000000000000000000000000
χ5444444444-2-4-4-4-4-2-2-2-2-2-2-2-4-4440000222-2-2-2-22000000220000000000000000000000000000000000000000
χ55444-44-4-4-4400004-44-44-4-400000000000000000000000000000000000000004-40000000000000000000000
χ56444-44-4-4-4400004-44-44-4-40000000000000000000000000000000000000000-440000000000000000000000
χ5744-44-4-44-440000-4-44-4-4440000000000000000000000000000000000000000004i−4i00000000000000000000
χ5844-44-4-44-440000-4-44-4-444000000000000000000000000000000000000000000−4i4i00000000000000000000
χ5944-4-4-44-44-2-4-4442-2-2-22224-4-4400002-2-222-2-22000000-220000000000000000000000000000000000000000
χ6044-4-4-44-44-2-4-4442-2-2-2222-444-400002-2-2-2-22220000002-20000000000000000000000000000000000000000
χ614-444-4-4-444-44-44-44-4-44-4400000000-4-4400004000000000000000000000000000000000000000000000000
χ624-444-4-4-44-24-44-42-222-22-200004i−4i4i−4i-2-220000200000000−2i2i−2i2i000000000000000000000000000000000000
χ634-444-4-4-44-24-44-42-222-22-20000−4i4i−4i4i-2-2200002000000002i−2i2i−2i000000000000000000000000000000000000
χ644-444-4-4-44-2-44-442-222-22-20000000022-20000-2000000000000−2i32i3−2i32i300000000000000000000000000000000
χ654-444-4-4-44-2-44-442-222-22-20000000022-20000-20000000000002i3−2i32i3−2i300000000000000000000000000000000
χ664-44-4-444-440000-4-4-4444-400000000000000000000−2i22i200000000000000−2i22i2−2i22i2000000000000000000000000
χ674-44-4-444-440000-4-4-4444-4000000000000000000002i2−2i2000000000000002i2−2i22i2−2i2000000000000000000000000
χ684-44-4-444-4-20000222-2-2-2200000000000−2i32i3−2i32i300000−2i22i200000000006−66−6i2−i2i2−i2000000000000000000000000
χ694-44-4-444-4-20000222-2-2-2200000000000−2i32i3−2i32i3000002i2−2i20000000000−66−66−i2i2−i2i2000000000000000000000000
χ704-44-4-444-4-20000222-2-2-22000000000002i3−2i32i3−2i300000−2i22i20000000000−66−66i2−i2i2−i2000000000000000000000000
χ714-44-4-444-4-20000222-2-2-22000000000002i3−2i32i3−2i3000002i2−2i200000000006−66−6−i2i2−i2i2000000000000000000000000
χ724-4-4444-4-4400004-4-44-4-44000000000000000000−2i22i2000000000000−2i22i22i2−2i20000000000000000000000000000
χ734-4-4444-4-4400004-4-44-4-440000000000000000002i2−2i20000000000002i2−2i2−2i22i20000000000000000000000000000
χ744-4-4444-4-4-20000-222-222-200000000000−2i32i32i3−2i3000−2i22i2000000000000i2−i2−i2i26−6−66000000000000000000000000
χ754-4-4444-4-4-20000-222-222-200000000000−2i32i32i3−2i30002i2−2i2000000000000−i2i2i2−i2−666−6000000000000000000000000
χ764-4-4444-4-4-20000-222-222-2000000000002i3−2i3−2i32i3000−2i22i2000000000000i2−i2−i2i2−666−6000000000000000000000000
χ774-4-4444-4-4-20000-222-222-2000000000002i3−2i3−2i32i30002i2−2i2000000000000−i2i2i2−i26−6−66000000000000000000000000
χ784-4-4-44-4444-444-444-4-4-44-400000000-44-400004000000000000000000000000000000000000000000000000
χ794-4-4-44-444-24-4-44-2-2222-2200004-4-44-22-20000200000000-222-2000000000000000000000000000000000000
χ804-4-4-44-444-24-4-44-2-2222-220000-444-4-22-200002000000002-2-22000000000000000000000000000000000000
χ814-4-4-44-444-2-444-4-2-2222-22000000002-220000-200000000000023−23−232300000000000000000000000000000000
χ824-4-4-44-444-2-444-4-2-2222-22000000002-220000-2000000000000−232323−2300000000000000000000000000000000
χ83888-88-8-8-8-40000-44-44-4440000000000000000000000000000000000000000000000000000000000000000
χ8488-88-8-88-8-4000044-444-4-40000000000000000000000000000000000000000000000000000000000000000

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