Finite Group Databasebeta

← Group #10858725

Character table — Group #10858725

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75
size111122222222224444444444444488888888888888888888121212121616161616161616162424242424242424242424242424
order122222344446662244444466121212124444661212121212121212121212121212888848812122424242422444444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-1111-1-1-1
χ4111111111111111111111111111111-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1111
χ5111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-111111111-1-11-1-111-1-1-1-11-11-1-1-1-1-11111
χ6111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-11-1-111-1-111-11-111111-1-1-1-1
χ7111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1-111-111-1-111-1-1111111-1-11-1-1-1
χ8111111111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-11111-1-1-1-1-1-111-1111
χ911111111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-111111111-11-1-1-1-1-111-1-1-11-11-1-11111-1-1
χ1011111111111111-1-1-1-11111111111-1-111-1-111-1-111-1-1-1-11111-1-1-1-1-11-1-1-1-1-111111-11-111-1-1-1-111
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11-111111-1-1-1-1-1-1-1-111111-111
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1111-111111-1-1111111-1-1-1-1-11-1-1
χ1311111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111111-1-111-1-1-1-111-1-1-1-111-1-111-1-1
χ1411111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-1-1-1-1-1-11111-1-111-1-111
χ1511111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1111111-11-11-1-1-1-11-111
χ1611111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-111-1-11111-1-11-11-11111-11-1-1
χ17222222-12222-1-1-122222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000222-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-122222222-1-1-1-1-1-122-2-2-1-1-1-1-1-1-1-1-1-1-1-111110000-2-2-211111100000000000000
χ19222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-2-222-1-111-1-1111111-1-1-1-10000-2-2211-1-11100000000000000
χ20222222-12222-1-1-12222-2-2-2-2-1-1-1-1-1-1-2-2-2-2-1-111-1-11111111111000022-2-1-111-1-100000000000000
χ21222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-2-22211-1-111-1-11111-1-1-1-10000-22-21111-1-100000000000000
χ22222222-12222-1-1-1-2-2-2-22222-1-1-1-1-1-1-2-2-2-211-1-111-1-11111111100002-22-1-1-1-11100000000000000
χ23222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1222211111111-1-1-1-1-1-1-1-100002-2-2-1-1111100000000000000
χ24222222-12222-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-122-2-211111111-1-1-1-111110000-22211-1-1-1-100000000000000
χ252222-2-222-2-22222000022-2-2-2-22-22-2000000-2-20022000000000022000000000000-20200000-200
χ262222-2-222-2-22222000022-2-2-2-22-22-2000000-2-200220000000000-2-200000000000020-200000200
χ272222-2-222-2-222220000-2-222-2-22-22-20000002200-2-200000000002200000000000020-200000-200
χ282222-2-222-2-222220000-2-222-2-22-22-20000002200-2-20000000000-2-2000000000000-20200000200
χ292222-2-22-222-222222-2-20000-2-2-22-2200002200-2-2000000000022000000000000020-200000-2000
χ302222-2-22-222-222222-2-20000-2-2-22-2200002200-2-20000000000-2-20000000000000-202000002000
χ312222-2-22-222-2222-2-2220000-2-2-22-220000-2-200220000000000220000000000000-20200000-2000
χ322222-2-22-222-2222-2-2220000-2-2-22-220000-2-200220000000000-2-2000000000000020-2000002000
χ3322-2-22-2222-2-2-22-22-22-200002-222-2-200002-2002-2000000000000000000000002-20000002-20000
χ3422-2-22-2222-2-2-22-22-22-200002-222-2-200002-2002-200000000000000000000000-22000000-220000
χ3522-2-22-2222-2-2-22-2-22-2200002-222-2-20000-2200-22000000000000000000000002-2000000-220000
χ3622-2-22-2222-2-2-22-2-22-2200002-222-2-20000-2200-2200000000000000000000000-220000002-20000
χ3722-2-22-22-2-222-22-200002i−2i2i−2i2-2-2-2220000002i−2i002i−2i0000000000000000000000000002i−2i00002-2
χ3822-2-22-22-2-222-22-200002i−2i2i−2i2-2-2-2220000002i−2i002i−2i000000000000000000000000000−2i2i0000-22
χ3922-2-22-22-2-222-22-20000−2i2i−2i2i2-2-2-222000000−2i2i00−2i2i0000000000000000000000000002i−2i0000-22
χ4022-2-22-22-2-222-22-20000−2i2i−2i2i2-2-2-222000000−2i2i00−2i2i000000000000000000000000000−2i2i00002-2
χ4122-2-2-222-22-22-22-22-2-222i−2i−2i2i-22-222-22i−2i002-2−2i2i-222i−2i2i2i−2i−2i0000000000000000000000000000000
χ4222-2-2-222-22-22-22-22-2-22−2i2i2i−2i-22-222-2−2i2i002-22i−2i-22−2i2i−2i−2i2i2i0000000000000000000000000000000
χ4322-2-2-222-22-22-22-2-222-22i−2i−2i2i-22-222-2−2i2i00-22−2i2i2-22i−2i−2i−2i2i2i0000000000000000000000000000000
χ4422-2-2-222-22-22-22-2-222-2−2i2i2i−2i-22-222-22i−2i00-222i−2i2-2−2i2i2i2i−2i−2i0000000000000000000000000000000
χ4522-2-2-22-1-22-221-112-2-222i−2i−2i2i1-11-1-112i−2i00-11i−i1-1−ii−i−iii−i3−i3i3i300000003−3−i3i33−300000000000000
χ4622-2-2-22-1-22-221-112-2-222i−2i−2i2i1-11-1-112i−2i00-11i−i1-1−ii−i−iiii3i3−i3−i30000000−33i3−i3−3300000000000000
χ4722-2-2-22-1-22-221-112-2-22−2i2i2i−2i1-11-1-11−2i2i00-11−ii1-1i−iii−i−i−i3−i3i3i30000000−33−i3i3−3300000000000000
χ4822-2-2-22-1-22-221-112-2-22−2i2i2i−2i1-11-1-11−2i2i00-11−ii1-1i−iii−i−ii3i3−i3−i300000003−3i3−i33−300000000000000
χ4922-2-2-22-1-22-221-11-222-22i−2i−2i2i1-11-1-11−2i2i001-1i−i-11−iiii−i−i−i3−i3i3i30000000−33i3−i33−300000000000000
χ5022-2-2-22-1-22-221-11-222-22i−2i−2i2i1-11-1-11−2i2i001-1i−i-11−iiii−i−ii3i3−i3−i300000003−3−i3i3−3300000000000000
χ5122-2-2-22-1-22-221-11-222-2−2i2i2i−2i1-11-1-112i−2i001-1−ii-11i−i−i−iii−i3−i3i3i300000003−3i3−i3−3300000000000000
χ5222-2-2-22-1-22-221-11-222-2−2i2i2i−2i1-11-1-112i−2i001-1−ii-11i−i−i−iiii3i3−i3−i30000000−33−i3i33−300000000000000
χ534444444-4-4-4-44440000000044-4-4-4-400000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-200000000-2-22222000000000000−2i32i3−2i32i30000000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-200000000-2-222220000000000002i3−2i32i3−2i30000000000000000000000000000000
χ564444-4-4-24-4-44-2-2-2000044-4-422-22-220000002200-2-200000000000000000000000000000000000
χ574444-4-4-24-4-44-2-2-20000-4-44422-22-22000000-2-2002200000000000000000000000000000000000
χ584444-4-4-2-444-4-2-2-244-4-40000222-22-20000-2-200220000000000000000000000000000000000000
χ594444-4-4-2-444-4-2-2-2-4-4440000222-22-200002200-2-20000000000000000000000000000000000000
χ6044-4-44-4-244-4-42-224-44-40000-22-2-2220000-2200-220000000000000000000000000000000000000
χ6144-4-44-4-244-4-42-22-44-440000-22-2-22200002-2002-20000000000000000000000000000000000000
χ6244-4-44-4-2-4-4442-2200004i−4i4i−4i-2222-2-2000000−2i2i00−2i2i00000000000000000000000000000000000
χ6344-4-44-4-2-4-4442-220000−4i4i−4i4i-2222-2-20000002i−2i002i−2i00000000000000000000000000000000000
χ6444-4-4-4444-44-4-44-400000000-444-4-4400000000000000000000000000000000000000000000000
χ6544-4-4-44-24-44-42-22000000002-2-222-200000000000023−23−23230000000000000000000000000000000
χ6644-4-4-44-24-44-42-22000000002-2-222-2000000000000−232323−230000000000000000000000000000000
χ674-4-4400400004-4-400000000000000002-20000000000002-22-2−2i22i2−2i22i200000000000000000000000
χ684-4-4400400004-4-400000000000000002-20000000000002-22-22i2−2i22i2−2i200000000000000000000000
χ694-4-4400400004-4-40000000000000000-22000000000000-22-22−2i22i22i2−2i200000000000000000000000
χ704-4-4400400004-4-40000000000000000-22000000000000-22-222i2−2i2−2i22i200000000000000000000000
χ718-88-80080000-8-880000000000000000000000000000000000000000000000000000000000000
χ728-88-800-4000044-4000000000000000000000000000000−2i32i32i3−2i3000000000000000000000000000
χ738-88-800-4000044-40000000000000000000000000000002i3−2i3−2i32i3000000000000000000000000000
χ748-8-8800-40000-44400000000000000004-4000000000000-22-22000000000000000000000000000
χ758-8-8800-40000-4440000000000000000-440000000000002-22-2000000000000000000000000000

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