Finite Group Databasebeta

← Group #10909583

Character table — Group #10909583

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444488888888888812121212161616161616161616161616161616242424242424242424244848
order122222344446666612121212224444441212121288884668812121212121224242424224488888844
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-1-1111-1-11111-1-1-1-1-1-11-11-1111-1-1-11-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-1-1-1-11-11-1-1-1111-11
χ5111111111111111111111-11-111-1-1-1-1-1-111-1-1-11-11-1-1-11-11111-1-111111-1-1-1-1-1-11
χ6111111111111111111111-11-111-1-1-1-1-1-1-1-111-11-11-1-1-11-11111-1-1-1-1-1-1-1111111-1
χ7111111111111111111111-11-1-1-11111111111-11-1-11-1-11-1-1-1-1-1111-11-11-1-1111-1-1
χ8111111111111111111111-11-1-1-1111111-1-1-1-1-11-1-11-1-11-1-1-1-1-111-11-11-111-1-1-111
χ911111111111111111111-11-1111-1-1-1-1-1-111-1-1-1-11-11-1-1-1111-1-111-1-1-1-111111-1-11
χ1011111111111111111111-11-1111-1-1-1-1-1-1-1-111-1-11-11-1-1-1111-1-1111111-1-1-1-1-111-1
χ1111111111111111111111-11-11-1-11111111111-1-111-1-1-1-11-1-111-1-1-11-11111-1-11-1-1
χ1211111111111111111111-11-11-1-1111111-1-1-1-1-1-111-1-1-1-11-1-111-1-11-11-1-1-1-111-111
χ1311111111111111111111-1-1-1-11111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-1-1-1111
χ1411111111111111111111-1-1-1-111111111-1-1-1-11-1-1-1-111-1-111-1-1-1-11111-11111-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-11111-1-1-1-11111-11-111-1-111-11-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-111111-11-1-111-1-11-11
χ17222222-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-100002-1-122-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2111100002-1-1-2-2-1-1-1-1111111000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-12-22-222-2-211110000-2-112-211-11-1-1-1-111000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-12-22-2-2-222-1-1-1-10000-2-11-2211-111111-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-22-2222-2-211110000-21-1-22111-1-1-111-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-22-22-2-222-1-1-1-10000-21-12-2111-111-1-111000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-10000211-2-2-1-111-1-11111000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111000021122-1-11111-1-1-1-1000000000000
χ252222-2-222-22-2222-2-22-22-2020-200000000002200200000-20000000-20200000-200
χ262222-2-222-22-2222-2-22-22-2020-20000000000-2-200200000-2000000020-200000200
χ272222-2-222-22-2222-2-22-22-20-20200000000002200-2000002000000020-200000-200
χ282222-2-222-22-2222-2-22-22-20-2020000000000-2-200-20000020000000-20200000200
χ292222-2-22-22-22222-2-2-22-2220-200000000022000200000-20000000-2020-20000000
χ302222-2-22-22-22222-2-2-22-2220-2000000000-2-2000200000-2000000020-2020000000
χ312222-2-22-22-22222-2-2-22-22-20200000000022000-2000002000000020-20-20000000
χ322222-2-22-22-22222-2-2-22-22-202000000000-2-2000-20000020000000-202020000000
χ332-22-22-2222-2-2-2-222-2-2-22200002-200000000000000000002-20000000002i−2i2i−2i000
χ342-22-22-2222-2-2-2-222-2-2-22200002-200000000000000000002-2000000000−2i2i−2i2i000
χ352-22-22-2222-2-2-2-222-2-2-2220000-220000000000000000000-220000000002i−2i−2i2i000
χ362-22-22-2222-2-2-2-222-2-2-2220000-220000000000000000000-22000000000−2i2i2i−2i000
χ374444444-4-4-4-444444-4-4-4-40000000000000000000000000000000000000000000
χ38444444-2-4-4-4-4-2-2-2-2-22222000000000000000000000−2i32i300000000000000000000
χ39444444-2-4-4-4-4-2-2-2-2-222220000000000000000000002i3−2i300000000000000000000
χ404444-4-4-24-44-4-2-2-222-22-22040-400000000000000-2000002000000000000000000
χ414444-4-4-24-44-4-2-2-222-22-220-40400000000000000200000-2000000000000000000
χ424444-4-4-2-44-44-2-2-2222-22-240-400000000000000-20000020000000000000000000
χ434444-4-4-2-44-44-2-2-2222-22-2-40400000000000000200000-20000000000000000000
χ444-44-44-44-4-444-4-444-444-4-40000000000000000000000000000000000000000000
χ454-44-44-4-244-4-422-2-2222-2-200004-40000000000000000000-220000000000000000
χ464-44-44-4-244-4-422-2-2222-2-20000-4400000000000000000002-20000000000000000
χ474-44-44-4-2-4-44422-2-22-2-222000000002323−23−230000000000000000000000000000000
χ484-44-44-4-2-4-44422-2-22-2-22200000000−23−2323230000000000000000000000000000000
χ494-44-4-4444-4-44-4-44-44-444-40000000000000000000000000000000000000000000
χ504-44-4-444-444-4-4-44-444-4-440000000000000000000000000000000000000000000
χ514-44-4-44-24-4-4422-22-22-2-2200000000000000000000000000000−2i32i3000000000000
χ524-44-4-44-24-4-4422-22-22-2-22000000000000000000000000000002i3−2i3000000000000
χ534-44-4-44-2-444-422-22-2-222-2000000000000000000000000000−2i32i300000000000000
χ544-44-4-44-2-444-422-22-2-222-20000000000000000000000000002i3−2i300000000000000
χ554-4-4400400004-4-40000000000002-22-22-2−2i22i2−2i22i2000000000000000000000000000
χ564-4-4400400004-4-40000000000002-22-22-22i2−2i22i2−2i2000000000000000000000000000
χ574-4-4400400004-4-4000000000000-22-22-22−2i22i22i2−2i2000000000000000000000000000
χ584-4-4400400004-4-4000000000000-22-22-222i2−2i2−2i22i2000000000000000000000000000
χ5988-8-80080000-88-80000000000000000000000000000000000000000000000000
χ6088-8-800-400004-440000000000000023−23−23230000000000000000000000000000000
χ6188-8-800-400004-4400000000000000−232323−230000000000000000000000000000000
χ628-8-8800-40000-4440000000000004-4-22-220000000000000000000000000000000
χ638-8-8800-40000-444000000000000-442-22-20000000000000000000000000000000

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