Finite Group Databasebeta

← Group #10909540

Character table — Group #10909540

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444488888888888812121212161616161616161616161616161616242424242424242424244848
order122222344446666612121212224444881212121288884466812121212121224242424222244888848
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-111-1-11-111-11111-1-1-1-1-1-1111-11-11-1-1-1-11
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1111-111-11111-1-1-1-1-1-1-1-1-11-11-11111-1
χ5111111111111111111111-11-1111111111111-1-11-1-11-1-1-1-1-111-1-1-1-1-11-1111-1-1-11
χ6111111111111111111111-11-111111111-1-1-1-1-1-11-1-11-1-1-1-1-111-1-1111-11-1-1-1111-1
χ7111111111111111111111-11-1-1-1-1-1-1-1-1-111-1-1-111-111-1-1-111-1-111-1-1-1-1-1-11-11111
χ8111111111111111111111-11-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-111-1-111111111-11-1-1-1-1
χ911111111111111111111-11-1111-1-111111111-1-1-111-11-1-1-1-1-1-1111-1-1-11-11111-1-1
χ1011111111111111111111-11-1111-1-11111-1-1-1-1-1-1-111-11-1-1-1-1-1-111-1111-11-1-1-1-111
χ1111111111111111111111-11-11-1-111-1-1-1-111-1-1-11-11-1-11-1-11111-1-11-1-11111-1-1-11-1
χ1211111111111111111111-11-11-1-111-1-1-1-1-1-111-11-11-1-11-1-11111-1-1-111-1-1-1-1111-11
χ1311111111111111111111-1-1-1-111-1-11111111111-1-1-1-1-11111-1-1-1-1-111-1-1-111-1-11-1
χ1411111111111111111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-11111-1-1-1-11-1-1111-1-111-11
χ1511111111111111111111-1-1-1-1-1-111-1-1-1-111-1-11-1-1-11-1-111-1-11111-1111-111-111-1-1
χ1611111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-11-1-111-1-111111-1-1-11-1-11-1-111
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
χ18222222-12222-1-1-1-1-1-1-1-1-12222-2-2-2-2111100002-2-1-1-2-1-1-1-1111111000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-12-22-22222-1-1-1-10000-2-2-11-2-111111-1-111000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-12-22-2-2-2-2-211110000-22-112-1111-1-111-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-22-2222-2-2-1-1-1-10000-2-21-121-1111111-1-1000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-22-22-2-22211110000-221-1-21-111-1-1-1-111000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-1-1-1-100002211-211-1-1-1-11111000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222111100002-211211-1-111-1-1-1-1000000000000
χ252222-2-222-2-22222-2-22-22-220-2000000000002200200-200000000000020-20-20000
χ262222-2-222-2-22222-2-22-22-220-200000000000-2-200200-2000000000000-202020000
χ272222-2-222-2-22222-2-22-22-2-202000000000002200-2002000000000000-2020-20000
χ282222-2-222-2-22222-2-22-22-2-20200000000000-2-200-200200000000000020-2020000
χ292222-2-22-222-2222-2-2-22-22020-2000000002200000200-2000000002000-20-200000
χ302222-2-22-222-2222-2-2-22-22020-200000000-2-200000200-200000000-200020200000
χ312222-2-22-222-2222-2-2-22-220-202000000002200000-200200000000-200020-200000
χ322222-2-22-222-2222-2-2-22-220-20200000000-2-200000-2002000000002000-20200000
χ332-22-22-2222-2-2-22-22-2-222-20000002i−2i00000000000000000002i−2i0002-2000002i−2i00
χ342-22-22-2222-2-2-22-22-2-222-20000002i−2i00000000000000000002i−2i000-2200000−2i2i00
χ352-22-22-2222-2-2-22-22-2-222-2000000−2i2i0000000000000000000−2i2i0002-200000−2i2i00
χ362-22-22-2222-2-2-22-22-2-222-2000000−2i2i0000000000000000000−2i2i000-22000002i−2i00
χ374444444-4-4-4-444444-4-4-4-40000000000000000000000000000000000000000000
χ38444444-2-4-4-4-4-2-2-2-2-2222200000000000000000000000−2i32i3000000000000000000
χ39444444-2-4-4-4-4-2-2-2-2-22222000000000000000000000002i3−2i3000000000000000000
χ404444-4-4-24-4-44-2-2-222-22-2240-4000000000000000-2002000000000000000000000
χ414444-4-4-24-4-44-2-2-222-22-22-404000000000000000200-2000000000000000000000
χ424444-4-4-2-444-4-2-2-2222-22-2040-4000000000000000-200200000000000000000000
χ434444-4-4-2-444-4-2-2-2222-22-20-404000000000000000200-200000000000000000000
χ444-44-44-44-4-444-44-44-44-4-440000000000000000000000000000000000000000000
χ454-44-44-4-244-4-42-22-222-2-220000004i−4i0000000000000000000−2i2i00000000000000
χ464-44-44-4-244-4-42-22-222-2-22000000−4i4i00000000000000000002i−2i00000000000000
χ474-44-44-4-2-4-4442-22-22-222-20000000000000000000000000000023−23000000000000
χ484-44-44-4-2-4-4442-22-22-222-200000000000000000000000000000−2323000000000000
χ494-44-4-4444-44-4-44-4-44-4-4440000000000000000000000000000000000000000000
χ504-44-4-444-44-44-44-4-4444-4-40000000000000000000000000000000000000000000
χ514-44-4-44-24-44-42-222-222-2-200000000−2i3−2i32i32i30000000000000000000000000000000
χ524-44-4-44-24-44-42-222-222-2-2000000002i32i3−2i3−2i30000000000000000000000000000000
χ534-44-4-44-2-44-442-222-2-2-222000000000000000000000000023−230000000000000000
χ544-44-4-44-2-44-442-222-2-2-2220000000000000000000000000−23230000000000000000
χ554-4-440040000-4-4400000000002-2002-22-222−2222−22000000000000000000000000000
χ564-4-440040000-4-4400000000002-2002-22-2−2222−2222000000000000000000000000000
χ574-4-440040000-4-440000000000-2200-22-2222−22−2222000000000000000000000000000
χ584-4-440040000-4-440000000000-2200-22-22−222222−22000000000000000000000000000
χ5988-8-800800008-8-80000000000000000000000000000000000000000000000000
χ6088-8-800-40000-44400000000000000−2i32i32i3−2i30000000000000000000000000000000
χ6188-8-800-40000-444000000000000002i3−2i3−2i32i30000000000000000000000000000000
χ628-8-8800-4000044-400000000004-400-22-220000000000000000000000000000000
χ638-8-8800-4000044-40000000000-44002-22-20000000000000000000000000000000

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