Finite Group Databasebeta

← Group #10945076

Character table — Group #10945076

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11112222222222444444444444444444668888888888888888881212121212121212121212121212121616161616161616162424484848
order12222222223666224444444444666666224466121212121212121212121212121222222444444444444412121212121244444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111
χ5111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1
χ6111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-11111-1-1-111
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1111111111-1-111-1-1-1-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-111111111-111-1-11111111-1-1
χ911111111111111-1-1-1-111-1-111-1-11111111111-1-11111-1-1-1-1-1-11111111-1-1-1-111-1-111-1-1-11-1-1-111-1-111-11-1
χ1011111111111111-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111-1-11-1111-1-111-1-11-11
χ1111111111111111-1-1-1-111-1-111-1-1111111-1-111-1-11111-1-1-1-1-1-11111-1-1-11111-1-111-1-111-11-1-1-111-1-1-1-11-11
χ1211111111111111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111-1111-1-11111-11-1
χ1311111111111111-1-1-1-1-1-111-1-1111111111111-1-1-1-1-1-11111-1-11111111-1-1-1-1-1-111-1-111-1-11-1-1-1-11111-1-11
χ1411111111111111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111-1-1-1-1-1-111-1-11111-11111-1-1-1-111-1
χ1511111111111111-1-1-1-1-1-111-1-111111111-1-111-1-1-1-1-1-11111-1-11111-1-1-1111111-1-111-1-1-1-11-1-1-1-111-1-111-1
χ1611111111111111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-111-1-111-11111-1-111-1-11
χ172222222222-1-1-1-1222222222222-1-1-1-1-1-10022-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000222-1-1-1-1-1-100000
χ182222222222-1-1-1-1222222222222-1-1-1-1-1-100-2-2-1-1-1-1-1-1-1-1-1-1-1-11111000000000000000-2-2-211111100000
χ192222222222-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-10022-1-111111111-1-1-1-1-1-10000000000000002-2-2-1-1111100000
χ202222222222-1-1-1-12222-2-2-2-2-2-2-2-2-1-1-1-1-1-100-2-2-1-111111111-1-11111000000000000000-22211-1-1-1-100000
χ212222222222-1-1-1-1-2-2-2-222-2-222-2-2-1-1-1-1-1-1002211-1-1-1-1111111-1-1-1-1000000000000000-22-211-1-11100000
χ222222222222-1-1-1-1-2-2-2-222-2-222-2-2-1-1-1-1-1-100-2-211-1-1-1-111111111110000000000000002-22-1-111-1-100000
χ232222222222-1-1-1-1-2-2-2-2-2-222-2-222-1-1-1-1-1-10022111111-1-1-1-111-1-1-1-1000000000000000-2-221111-1-100000
χ242222222222-1-1-1-1-2-2-2-2-2-222-2-222-1-1-1-1-1-100-2-2111111-1-1-1-111111100000000000000022-2-1-1-1-11100000
χ2522222-2-22-2-222220000002200-2-22-2-22-2-2220000000022-2-20000002-2-20000002200-2-200000000000000
χ2622222-2-22-2-222220000002200-2-22-2-22-2-2-2-20000000022-2-2000000-222000000-2-2002200000000000000
χ2722222-2-22-2-22222000000-2-200222-2-22-2-22200000000-2-2220000002-2-2000000-2-2002200000000000000
χ2822222-2-22-2-22222000000-2-200222-2-22-2-2-2-200000000-2-222000000-2220000002200-2-200000000000000
χ292222-22-2-22-2222200002200-2-200-22-2-22-222000022-2-20000000000-22-200002200-2-20000000000000000
χ302222-22-2-22-2222200002200-2-200-22-2-22-2-2-2000022-2-200000000002-220000-2-200220000000000000000
χ312222-22-2-22-222220000-2-2002200-22-2-22-2220000-2-2220000000000-22-20000-2-200220000000000000000
χ322222-22-2-22-222220000-2-2002200-22-2-22-2-2-20000-2-22200000000002-2200002200-2-20000000000000000
χ332222-2-22-2-22222222-2-200000000-2-22-2-2222002200000000-2-20000-2-2222-2-20000000000000000000000
χ342222-2-22-2-22222222-2-200000000-2-22-2-22-2-2002200000000-2-2000022-2-2-2220000000000000000000000
χ352222-2-22-2-222222-2-22200000000-2-22-2-222200-2-200000000220000-2-22-2-2220000000000000000000000
χ362222-2-22-2-222222-2-22200000000-2-22-2-22-2-200-2-20000000022000022-222-2-20000000000000000000000
χ3722-2-2222-2-2-22-2-222-22-200000000-2-2-222200002-2000000002-2000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ3822-2-2222-2-2-22-2-222-22-200000000-2-2-222200002-2000000002-200000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ3922-2-2222-2-2-22-2-22-22-2200000000-2-2-22220000-2200000000-22000000000002i−2i−2i2i2i−2i−2i2i00000000000000
χ4022-2-2222-2-2-22-2-22-22-2200000000-2-2-22220000-2200000000-2200000000000−2i2i2i−2i−2i2i2i−2i00000000000000
χ4122-2-22-2-2-2222-2-2200002i−2i002i−2i00-2222-2-20000002i−2i2i−2i00000000000002-22-2002i−2i00−2i2i00000000000000
χ4222-2-22-2-2-2222-2-2200002i−2i002i−2i00-2222-2-20000002i−2i2i−2i0000000000000-22-2200−2i2i002i−2i00000000000000
χ4322-2-22-2-2-2222-2-220000−2i2i00−2i2i00-2222-2-2000000−2i2i−2i2i00000000000002-22-200−2i2i002i−2i00000000000000
χ4422-2-22-2-2-2222-2-220000−2i2i00−2i2i00-2222-2-2000000−2i2i−2i2i0000000000000-22-22002i−2i00−2i2i00000000000000
χ4522-2-2-22-22-222-2-220000002i−2i002i−2i2-22-22-200000000002i−2i2i−2i0000000002-2-222i−2i00−2i2i0000000000000000
χ4622-2-2-22-22-222-2-220000002i−2i002i−2i2-22-22-200000000002i−2i2i−2i000000000-222-2−2i2i002i−2i0000000000000000
χ4722-2-2-22-22-222-2-22000000−2i2i00−2i2i2-22-22-20000000000−2i2i−2i2i0000000002-2-22−2i2i002i−2i0000000000000000
χ4822-2-2-22-22-222-2-22000000−2i2i00−2i2i2-22-22-20000000000−2i2i−2i2i000000000-222-22i−2i00−2i2i0000000000000000
χ4922-2-2-2-2222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i22-2-2-2200002-22i−2i−2i2i2i−2i−2i2i-22000000000000000000000000000000000
χ5022-2-2-2-2222-22-2-222-2-22−2i2i−2i2i2i−2i2i−2i22-2-2-2200002-2−2i2i2i−2i−2i2i2i−2i-22000000000000000000000000000000000
χ5122-2-2-2-2222-22-2-22-222-22i−2i−2i2i−2i2i2i−2i22-2-2-220000-222i−2i−2i2i−2i2i2i−2i2-2000000000000000000000000000000000
χ5222-2-2-2-2222-22-2-22-222-2−2i2i2i−2i2i−2i−2i2i22-2-2-220000-22−2i2i2i−2i2i−2i−2i2i2-2000000000000000000000000000000000
χ5322-2-2-2-2222-2-111-12-2-222i−2i2i−2i−2i2i−2i2i-1-1111-10000-11−iii−i−iii−i1-1−i3−i3i3i3000000000000000000−i3i33−33−300000
χ5422-2-2-2-2222-2-111-12-2-222i−2i2i−2i−2i2i−2i2i-1-1111-10000-11−iii−i−iii−i1-1i3i3−i3−i3000000000000000000i3−i3−33−3300000
χ5522-2-2-2-2222-2-111-12-2-22−2i2i−2i2i2i−2i2i−2i-1-1111-10000-11i−i−iii−i−ii1-1−i3−i3i3i3000000000000000000−i3i3−33−3300000
χ5622-2-2-2-2222-2-111-12-2-22−2i2i−2i2i2i−2i2i−2i-1-1111-10000-11i−i−iii−i−ii1-1i3i3−i3−i3000000000000000000i3−i33−33−300000
χ5722-2-2-2-2222-2-111-1-222-22i−2i−2i2i−2i2i2i−2i-1-1111-100001-1−iii−ii−i−ii-11−i3−i3i3i3000000000000000000i3−i33−3−3300000
χ5822-2-2-2-2222-2-111-1-222-22i−2i−2i2i−2i2i2i−2i-1-1111-100001-1−iii−ii−i−ii-11i3i3−i3−i3000000000000000000−i3i3−333−300000
χ5922-2-2-2-2222-2-111-1-222-2−2i2i2i−2i2i−2i−2i2i-1-1111-100001-1i−i−ii−iii−i-11−i3−i3i3i3000000000000000000i3−i3−333−300000
χ6022-2-2-2-2222-2-111-1-222-2−2i2i2i−2i2i−2i−2i2i-1-1111-100001-1i−i−ii−iii−i-11i3i3−i3−i3000000000000000000−i3i33−3−3300000
χ6144444-4-44-4-4-2-2-2-20000004400-4-4-222-2220000000000-2-22200000000000000000000000000000000000
χ6244444-4-44-4-4-2-2-2-2000000-4-40044-222-222000000000022-2-200000000000000000000000000000000000
χ634444-44-4-44-4-2-2-2-200004400-4-4002-222-22000000-2-222000000000000000000000000000000000000000
χ644444-44-4-44-4-2-2-2-20000-4-40044002-222-2200000022-2-2000000000000000000000000000000000000000
χ654444-4-44-4-44-2-2-2-244-4-40000000022-222-20000-2-20000000022000000000000000000000000000000000
χ664444-4-44-4-44-2-2-2-2-4-4440000000022-222-200002200000000-2-2000000000000000000000000000000000
χ6744-4-4444-4-4-4-222-24-44-400000000222-2-2-20000-2200000000-22000000000000000000000000000000000
χ6844-4-4444-4-4-4-222-2-44-4400000000222-2-2-200002-2000000002-2000000000000000000000000000000000
χ6944-4-44-4-4-444-222-200004i−4i004i−4i002-2-2-222000000−2i2i−2i2i000000000000000000000000000000000000000
χ7044-4-44-4-4-444-222-20000−4i4i00−4i4i002-2-2-2220000002i−2i2i−2i000000000000000000000000000000000000000
χ7144-4-4-44-44-44-222-20000004i−4i004i−4i-22-22-220000000000−2i2i−2i2i00000000000000000000000000000000000
χ7244-4-4-44-44-44-222-2000000−4i4i00−4i4i-22-22-2200000000002i−2i2i−2i00000000000000000000000000000000000
χ734-44-400000044-4-40000000000000000004-42i−2i0000000000002i−2i2i−2i0000000000000000000000002i−2i000
χ744-44-400000044-4-40000000000000000004-4−2i2i000000000000−2i2i−2i2i000000000000000000000000−2i2i000
χ754-44-400000044-4-4000000000000000000-442i−2i0000000000002i−2i2i−2i000000000000000000000000−2i2i000
χ764-44-400000044-4-4000000000000000000-44−2i2i000000000000−2i2i−2i2i0000000000000000000000002i−2i000
χ778-88-8000000-4-444000000000000000000004i−4i000000000000−2i2i−2i2i00000000000000000000000000000
χ788-88-8000000-4-44400000000000000000000−4i4i0000000000002i−2i2i−2i00000000000000000000000000000
χ798-8-880000008-88-80000000000000000000000000000000000000000000000000000000000000000000
χ808-8-88000000-44-44000000000000000000000000000000000023−23−232300000000000000000000000000000
χ818-8-88000000-44-440000000000000000000000000000000000−232323−2300000000000000000000000000000

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