Finite Group Databasebeta

← Group #10909577

Character table — Group #10909577

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444488888888888812121212161616161616161616161616161616242424242424242424244848
order122222344446666612121212224444881212121288884466812121212121224242424222244888848
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-1-11-111-111-1-111-1-1-1-1111-11-11-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-111-111-1-111-1-1-1-1-1-1-11-11-11111-1
χ5111111111111111111111-11-1111111111111-1-11-1-1-1-1-1-11-111-1-1-1-1-11-1111-1-1-11
χ6111111111111111111111-11-111111111-1-1-1-1-1-11-1-1-1-1-1-11-111-1-1111-11-1-1-1111-1
χ7111111111111111111111-11-1-1-1-1-1-1-1-1-111-1-1-111-11-1-1111-1-1-111-1-1-1-1-1-11-11111
χ8111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-111-11-1-1111-1-1-111111111-11-1-1-1-1
χ911111111111111111111-11-1111-1-111111111-1-1-111-1-1-1-1-11-1-1111-1-1-11-11111-1-1
χ1011111111111111111111-11-1111-1-11111-1-1-1-1-1-1-111-1-1-1-1-11-1-111-1111-11-1-1-1-111
χ1111111111111111111111-11-11-1-111-1-1-1-111-1-1-11-11-1-1-111-1111-1-11-1-11111-1-1-11-1
χ1211111111111111111111-11-11-1-111-1-1-1-1-1-111-11-11-1-1-111-1111-1-1-111-1-1-1-1111-11
χ1311111111111111111111-1-1-1-111-1-11111111111-1-1-11111-1-1-1-1-1-1-111-1-1-111-1-11-1
χ1411111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-11111-1-1-1-1-1-11-1-1111-1-111-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11-1-1-1111-1-1-1-11111-1111-111-111-1-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1111-1-1-1-111111-1-1-11-1-11-1-111
χ17222222-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-1000022-1-12-1-1-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2111100002-2-1-1-2-1-111-1-11111000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-12-22-22222-1-1-1-10000-2-2-11-21111-11-1-111000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-12-22-2-2-2-2-211110000-22-11211-1-1-1111-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-22-2222-2-2-1-1-1-10000-2-21-1211111-111-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-22-22-2-22211110000-221-1-211-1-11-1-1-111000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-100002211-2-1-1-1-1111111000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222111100002-2112-1-11111-1-1-1-1000000000000
χ252222-2-222-2-22222-2-22-22-220-20000000000022002000000-200000000-2020-20000
χ262222-2-222-2-22222-2-22-22-220-200000000000-2-2002000000-20000000020-2020000
χ272222-2-222-2-22222-2-22-22-2-202000000000002200-200000020000000020-20-20000
χ282222-2-222-2-22222-2-22-22-2-20200000000000-2-200-2000000200000000-202020000
χ292222-2-22-222-2222-2-2-22-22020-20000000022000002000000-200002000-20-200000
χ302222-2-22-222-2222-2-2-22-22020-200000000-2-2000002000000-20000-200020200000
χ312222-2-22-222-2222-2-2-22-220-202000000002200000-200000020000-200020-200000
χ322222-2-22-222-2222-2-2-22-220-20200000000-2-200000-2000000200002000-20200000
χ332-2-222-2222-2-2-2-222-2-222-20000002i−2i00000000000000000002i−2i0002-2000002i−2i00
χ342-2-222-2222-2-2-2-222-2-222-20000002i−2i00000000000000000002i−2i000-2200000−2i2i00
χ352-2-222-2222-2-2-2-222-2-222-2000000−2i2i0000000000000000000−2i2i0002-200000−2i2i00
χ362-2-222-2222-2-2-2-222-2-222-2000000−2i2i0000000000000000000−2i2i000-22000002i−2i00
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
χ404444-4-4-24-4-44-2-2-222-22-2240-4000000000000000-2000000200000000000000000
χ414444-4-4-24-4-44-2-2-222-22-22-4040000000000000002000000-200000000000000000
χ424444-4-4-2-444-4-2-2-2222-22-2040-4000000000000000-200000020000000000000000
χ434444-4-4-2-444-4-2-2-2222-22-20-4040000000000000002000000-20000000000000000
χ4444-4-400400004-4-400000000002i−2i002i2i−2i−2i22−22−2i22i2000000000000000000000000000
χ4544-4-400400004-4-400000000002i−2i002i2i−2i−2i−22222i2−2i2000000000000000000000000000
χ4644-4-400400004-4-40000000000−2i2i00−2i−2i2i2i22−222i2−2i2000000000000000000000000000
χ4744-4-400400004-4-40000000000−2i2i00−2i−2i2i2i−2222−2i22i2000000000000000000000000000
χ484-4-444-44-4-444-4-444-44-4-440000000000000000000000000000000000000000000
χ494-4-444-4-244-4-422-2-222-2-220000004i−4i0000000000000000000−2i2i00000000000000
χ504-4-444-4-244-4-422-2-222-2-22000000−4i4i00000000000000000002i−2i00000000000000
χ514-4-444-4-2-4-44422-2-22-222-20000000000000000000000000000023−23000000000000
χ524-4-444-4-2-4-44422-2-22-222-200000000000000000000000000000−2323000000000000
χ534-4-44-4444-44-4-4-44-44-4-4440000000000000000000000000000000000000000000
χ544-4-44-444-44-44-4-44-4444-4-40000000000000000000000000000000000000000000
χ554-4-44-44-24-44-422-22-222-2-200000000−2i32i3−2i32i30000000000000000000000000000000
χ564-4-44-44-24-44-422-22-222-2-2000000002i3−2i32i3−2i30000000000000000000000000000000
χ574-4-44-44-2-44-4422-22-2-2-2220000000000000000000000023−23000000000000000000
χ584-4-44-44-2-44-4422-22-2-2-22200000000000000000000000−2323000000000000000000
χ5988-8-800-40000-44400000000004i−4i00−2i−2i2i2i0000000000000000000000000000000
χ6088-8-800-40000-4440000000000−4i4i002i2i−2i−2i0000000000000000000000000000000
χ618-88-80080000-88-80000000000000000000000000000000000000000000000000
χ628-88-800-400004-440000000000000023−23−23230000000000000000000000000000000
χ638-88-800-400004-4400000000000000−232323−230000000000000000000000000000000

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