Finite Group Databasebeta

← Group #10909568

Character table — Group #10909568

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63
size1111222222222244444488888888888812121212161616161616161616161616161616242424242424242424244848
order1222223444466666121212122222444412121212888846666881212121224242424224488888844
χ1111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111-11-1-1-1-1-1-1-111-1-1-1111-11-1-1-11-111-1-111111-1-1-1-1-11-1
χ411111111111111111111111-11-1-1-1-1-1-1-1-1-111-1111-11-1-1-11-111-1-1-1-1-1-1-111111-11
χ51111111111111111111111-11-11-1-1-1-1-1-111-1-1-111-11-11-1-1-11-1-111-1-1-1-111111-11-1
χ61111111111111111111111-11-11-1-1-1-1-1-1-1-111-111-11-11-1-1-11-1-1111111-1-1-1-1-11-11
χ71111111111111111111111-1-1-1-11111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111
χ81111111111111111111111-1-1-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-1-1-11111-11111-1-1-1
χ911111111111111111111-1-11111-1-1-1-1-1-111-1-11-1-111-1-11111-1-1-1-11-11-1111-1-1-1-11
χ1011111111111111111111-1-11111-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1-11-11-1-1-11111-1
χ1111111111111111111111-1-11-11-11111111111-1-1-11-1-11-1-11-1-1-1111-11-11-1-1111-1-1
χ1211111111111111111111-1-11-11-1111111-1-1-1-1-1-1-11-1-11-1-11-1-1-111-11-11-111-1-1-111
χ1311111111111111111111-1-1-11-111111111111-1-1-1-111-1-1-1-1111-1-1-11-11111-1-11-1-1
χ1411111111111111111111-1-1-11-11111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-11-11-1-1-1-111-111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-11111-1-11111-11-111-1-111-1-11
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-1-111111-11-1-111-1-111-1
χ17222222-12222-1-1-1-1-1-1-1-1-122222222-1-1-1-100002-1-1-1-122-1-1-1-1-1-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-1-1-1222-22-2-2-211110000-2-1-1-112-211-11-1-111000000000000
χ19222222-12222-1-1-1-1-1-1-1-1-122-22-22-2-211110000-2-1-11-1-22111-111-1-1000000000000
χ20222222-12222-1-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-100002-1-111-2-2-1-1111111000000000000
χ21222222-12222-1-1-1-1-1-1-1-1-1-2-22222-2-211110000211-1-1-2-2-1-1-1-11111000000000000
χ22222222-12222-1-1-1-1-1-1-1-1-1-2-22-22-222-1-1-1-10000-211-11-2211-1111-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-1-1-1-2-2-22-2222-1-1-1-10000-2111-12-2111-1-1-111000000000000
χ24222222-12222-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111100002111122-1-111-1-1-1-1000000000000
χ252222-2-222-22-2222-2-22-22-200020-200000000220000200000-200000-20200000-200
χ262222-2-222-22-2222-2-22-22-200020-200000000-2-20000200000-20000020-200000200
χ272222-2-222-22-2222-2-22-22-2000-20200000000220000-20000020000020-200000-200
χ282222-2-222-22-2222-2-22-22-2000-20200000000-2-20000-200000200000-20200000200
χ292222-2-22-22-22222-2-2-22-220020-200000002200000200000-20000020-20-20000000
χ302222-2-22-22-22222-2-2-22-220020-20000000-2-200000200000-200000-202020000000
χ312222-2-22-22-22222-2-2-22-2200-20200000002200000-200000200000-2020-20000000
χ322222-2-22-22-22222-2-2-22-2200-2020000000-2-200000-20000020000020-2020000000
χ332-2-222-2222-2-2-2-222-2-2-2222-20000000000000002-2000000000000000002i−2i2i−2i000
χ342-2-222-2222-2-2-2-222-2-2-2222-20000000000000002-200000000000000000−2i2i−2i2i000
χ352-2-222-2222-2-2-2-222-2-2-222-22000000000000000-22000000000000000002i−2i−2i2i000
χ362-2-222-2222-2-2-2-222-2-2-222-22000000000000000-2200000000000000000−2i2i2i−2i000
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
χ404444-4-4-24-44-4-2-2-222-22-2200040-400000000000000-20000020000000000000000
χ414444-4-4-24-44-4-2-2-222-22-22000-40400000000000000200000-20000000000000000
χ424444-4-4-2-44-44-2-2-2222-22-20040-400000000000000-200000200000000000000000
χ434444-4-4-2-44-44-2-2-2222-22-200-40400000000000000200000-200000000000000000
χ4444-4-400400004-4-40000000000002i−2i2i2i−2i−2i22−22−2i22i2000000000000000000000000000
χ4544-4-400400004-4-40000000000002i−2i2i2i−2i−2i−22222i2−2i2000000000000000000000000000
χ4644-4-400400004-4-4000000000000−2i2i−2i−2i2i2i22−222i2−2i2000000000000000000000000000
χ4744-4-400400004-4-4000000000000−2i2i−2i−2i2i2i−2222−2i22i2000000000000000000000000000
χ484-4-444-44-4-444-4-444-444-4-40000000000000000000000000000000000000000000
χ494-4-444-4-244-4-422-2-2222-2-24-4000000000000000-22000000000000000000000000
χ504-4-444-4-244-4-422-2-2222-2-2-440000000000000002-2000000000000000000000000
χ514-4-444-4-2-4-44422-2-22-2-2220000000023−2323−230000000000000000000000000000000
χ524-4-444-4-2-4-44422-2-22-2-22200000000−2323−23230000000000000000000000000000000
χ534-4-44-4444-4-44-4-44-44-444-40000000000000000000000000000000000000000000
χ544-4-44-444-444-4-4-44-444-4-440000000000000000000000000000000000000000000
χ554-4-44-44-24-4-4422-22-22-2-2200000000000000000000000000000−2i32i3000000000000
χ564-4-44-44-24-4-4422-22-22-2-22000000000000000000000000000002i3−2i3000000000000
χ574-4-44-44-2-444-422-22-2-222-2000000000000000000000000000−2i32i300000000000000
χ584-4-44-44-2-444-422-22-2-222-20000000000000000000000000002i3−2i300000000000000
χ5988-8-800-40000-4440000000000004i−4i−2i−2i2i2i0000000000000000000000000000000
χ6088-8-800-40000-444000000000000−4i4i2i2i−2i−2i0000000000000000000000000000000
χ618-88-80080000-88-80000000000000000000000000000000000000000000000000
χ628-88-800-400004-4400000000000000−2i32i32i3−2i30000000000000000000000000000000
χ638-88-800-400004-44000000000000002i3−2i3−2i32i30000000000000000000000000000000

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