Finite Group Databasebeta

← Group #10828705

Character table — Group #10828705

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size11112222222222444444444466888888888888888888888888881212121616161616161624242424242424242424242448
order1222223444466644446612121212442244444466668812121212121212121212121222481212242424242444444444888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11-1-11111-1-111111111-1-1-1-1111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1111-11111-1-1-11-11-1-111-1-111-1
χ411111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-111111111-1-1-1-111-11-11-1-1-1-111-1-11
χ5111111111111111111111111-1-111111111111111111111111111-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111
χ7111111111111111111111111-1-1-1-1-111-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11-11-111-1-111-1-11
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111-1-11111-1-1-11-1-1-1-1111-11-11111-1-111-1
χ911111111111111-1-1-1-11111111111-111-1111111-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-1-1-1-1-1111111-1-1-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-1111
χ1111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-1111-11-1-1-111-1-1-1-11
χ1211111111111111-1-1-1-111111111-1-11-1-1111-1-1-1-111-1-111-1-1111111111-1-1-111-1-11-11-1-1-1-1-11111-1
χ1311111111111111-1-1-1-1111111-1-111-111-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1111
χ1411111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111111-1-11111-1-1-1
χ1511111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1111-1-111-11-1111-1-11111-1
χ1611111111111111-1-1-1-1111111-1-1-1-11-1-1111-1-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-11-111111-1-1-1-11
χ172222222-2-2-2-2222000022-2-2-2-2222-200000022-2-200000000000000-2-22000000000002-20000000
χ182222222-2-2-2-2222000022-2-2-2-222-22000000-2-22200000000000000-2-2200000000000-220000000
χ192222222-2-2-2-2222000022-2-2-2-2-2-22-200000022-2-20000000000000022-200000000000-220000000
χ202222222-2-2-2-2222000022-2-2-2-2-2-2-22000000-2-2220000000000000022-2000000000002-20000000
χ21222222-12222-1-1-12222-1-1-1-1-1-10022222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-10002-1-1-1-1-1-10000000000000
χ22222222-12222-1-1-12222-1-1-1-1-1-100222-2-22-2-2-1-1-1-1-2-2-1-1-1-1-1-1-1-11111000-21111110000000000000
χ23222222-12222-1-1-12222-1-1-1-1-1-100-2-2-222-2-2-2111122-1-111-1-1111111000-2-1-1-1-1110000000000000
χ24222222-12222-1-1-12222-1-1-1-1-1-100-2-2-2-2-2-2221111-2-2-1-111-1-111-1-1-1-100021111-1-10000000000000
χ25222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-10022-222-222-1-1-1-1-2-211111111-1-1-1-1000-2-1-111110000000000000
χ26222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-10022-2-2-2-2-2-2-1-1-1-122111111111111000211-1-1-1-10000000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-2-22222-2-21111-2-211-1-111-1-111110002-1-111-1-10000000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-1-1-1-100-2-22-2-222211112211-1-111-1-1-1-1-1-1000-211-1-1110000000000000
χ292222-2-222-2-2222222-2-2-2-22-22-22200000000000000-2-200220000002-2-200000000-202000000000
χ302222-2-222-2-2222222-2-2-2-22-22-2-2-200000000000000-2-20022000000-2220000000020-2000000000
χ312222-2-222-2-22222-2-222-2-22-22-222000000000000002200-2-20000002-2-20000000020-2000000000
χ322222-2-222-2-22222-2-222-2-22-22-2-2-2000000000000002200-2-2000000-22200000000-202000000000
χ332222-2-22-222-22220000-2-2-22-222200200-20000000000-2-200220000-22-20000000-2020000000000
χ342222-2-22-222-22220000-2-2-22-222200-200200000000002200-2-20000-22-2000000020-20000000000
χ352222-2-22-222-22220000-2-2-22-22-2-200200-20000000000-2-2002200002-22000000020-20000000000
χ362222-2-22-222-22220000-2-2-22-22-2-200-200200000000002200-2-200002-220000000-2020000000000
χ3722-2-22-22-2-2222-2-22i−2i2i−2i-22-222-200000000000000002i−2i002i−2i00000000000000000000002i−2i002-20
χ3822-2-22-22-2-2222-2-22i−2i2i−2i-22-222-200000000000000002i−2i002i−2i0000000000000000000000−2i2i00-220
χ3922-2-22-22-2-2222-2-2−2i2i−2i2i-22-222-20000000000000000−2i2i00−2i2i00000000000000000000002i−2i00-220
χ4022-2-22-22-2-2222-2-2−2i2i−2i2i-22-222-20000000000000000−2i2i00−2i2i0000000000000000000000−2i2i002-20
χ4122-2-2-222-22-222-2-22i−2i−2i2i2-2-2-222000002i−2i00000002-2−2i2i002i−2i00000000002i−2i2-2000000000000000
χ4222-2-2-222-22-222-2-22i−2i−2i2i2-2-2-22200000−2i2i0000000-22−2i2i002i−2i0000000000−2i2i-22000000000000000
χ4322-2-2-222-22-222-2-2−2i2i2i−2i2-2-2-222000002i−2i0000000-222i−2i00−2i2i00000000002i−2i-22000000000000000
χ4422-2-2-222-22-222-2-2−2i2i2i−2i2-2-2-22200000−2i2i00000002-22i−2i00−2i2i0000000000−2i2i2-2000000000000000
χ4522-2-2-22-1-22-22-1112i−2i−2i2i-1111-1-1000002i−2i000−i3i3−i3i32-2i−i3−3−ii3−333−3−30000−ii-11−i3i30000000000000
χ4622-2-2-22-1-22-22-1112i−2i−2i2i-1111-1-1000002i−2i000i3−i3i3−i32-2i−i−33−ii−33−3−3330000−ii-11i3−i30000000000000
χ4722-2-2-22-1-22-22-1112i−2i−2i2i-1111-1-100000−2i2i000−i3i3−i3i3-22i−i3−3−ii3−3−3−3330000i−i1-1i3−i30000000000000
χ4822-2-2-22-1-22-22-1112i−2i−2i2i-1111-1-100000−2i2i000i3−i3i3−i3-22i−i−33−ii−3333−3−30000i−i1-1−i3i30000000000000
χ4922-2-2-22-1-22-22-111−2i2i2i−2i-1111-1-1000002i−2i000−i3i3−i3i3-22−ii−33i−i−3333−3−30000−ii1-1i3−i30000000000000
χ5022-2-2-22-1-22-22-111−2i2i2i−2i-1111-1-1000002i−2i000i3−i3i3−i3-22−ii3−3i−i3−3−3−3330000−ii1-1−i3i30000000000000
χ5122-2-2-22-1-22-22-111−2i2i2i−2i-1111-1-100000−2i2i000−i3i3−i3i32-2−ii−33i−i−33−3−3330000i−i-11−i3i30000000000000
χ5222-2-2-22-1-22-22-111−2i2i2i−2i-1111-1-100000−2i2i000i3−i3i3−i32-2−ii3−3i−i3−333−3−30000i−i-11i3−i30000000000000
χ53444444-2-4-4-4-4-2-2-20000-2-22222004-4000000-2-2220000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-20000-2-2222200-4400000022-2-20000000000000000000000000000000000000
χ554444-4-4-24-4-44-2-2-244-4-422-22-2200000000000000002200-2-200000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2-4-44422-22-220000000000000000-2-2002200000000000000000000000000000
χ574444-4-4-2-444-4-2-2-20000222-22-20000400-400000000002200-2-2000000000000000000000000000
χ584444-4-4-2-444-4-2-2-20000222-22-20000-40040000000000-2-20022000000000000000000000000000
χ5944-4-44-4444-4-44-4-40000-444-4-44000000000000000000000000000000000000000000000000000
χ6044-4-44-4-244-4-4-22200002-2-222-200000000000000000023−2300−2323000000000000000000000000000
χ6144-4-44-4-244-4-4-22200002-2-222-2000000000000000000−23230023−23000000000000000000000000000
χ6244-4-44-4-2-4-444-2224i−4i4i−4i2-22-2-220000000000000000−2i2i00−2i2i00000000000000000000000000000
χ6344-4-44-4-2-4-444-222−4i4i−4i4i2-22-2-2200000000000000002i−2i002i−2i00000000000000000000000000000
χ6444-4-4-4444-44-44-4-400004-444-4-4000000000000000000000000000000000000000000000000000
χ6544-4-4-44-24-44-4-2220000-22-2-2220000000000−2i32i32i3−2i30000000000000000000000000000000000000
χ6644-4-4-44-24-44-4-2220000-22-2-22200000000002i3−2i3−2i32i30000000000000000000000000000000000000
χ674-44-40040000-4-4400000000004i−4i0000002-2000000000000002-22-20000000000000000002i−2i000
χ684-44-40040000-4-4400000000004i−4i000000-2200000000000000-22-22000000000000000000−2i2i000
χ694-44-40040000-4-440000000000−4i4i0000002-2000000000000002-22-2000000000000000000−2i2i000
χ704-44-40040000-4-440000000000−4i4i000000-2200000000000000-22-220000000000000000002i−2i000
χ718-88-800-4000044-40000000000000000004-400000000000000-22-2200000000000000000000000
χ728-88-800-4000044-4000000000000000000-44000000000000002-22-200000000000000000000000
χ738-8-880080000-88-80000000000000000000000000000000000000000000000000000000000000
χ748-8-8800-400004-44000000000000000000000000000000000023−23−232300000000000000000000000
χ758-8-8800-400004-440000000000000000000000000000000000−232323−2300000000000000000000000

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