Finite Group Databasebeta

← Group #10909542

Character table — Group #10909542

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size1111222222222222224444444488888888888888888816161616161616161616162424242424242424242424244848
order1222223444466666668888121212122244881212121224242424242424244446612121212121222224444888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11-1
χ411111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-11
χ511111111111111111111-1-1111111-1-11-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1111-1111-1-1-1-1-1-11
χ611111111111111111111-1-1111111-1-11-1-1-1-1-11111-1-1-1-11-1-11111-1-1-1-1-1-1-11-1-1-1111111-1
χ711111111111111111111-1-11111-1-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-1-1-1111111-1111-11-1-111-1-1
χ811111111111111111111-1-11111-1-1-1-11-1-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-11-1-1-11-111-1-111
χ9111111111111111111-1-111111111-1-1-11-1-1-1-1-1-1-1-11111-11-111-1-111-1-11-1111-111-1-1-1-11-1
χ10111111111111111111-1-111111111-1-1-11-1-1-1-1-1-1-1-11111-11-111-1-111-1-1-11-1-1-11-1-11111-11
χ11111111111111111111-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-1111-1-1-11-1-1-1-1-11111
χ12111111111111111111-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-111111-11-1-111-1-111-1111-111111-1-1-1-1
χ13111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111-11-11-11-11111-1-1
χ14111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-11-11-11-11-1-1-1-111
χ15111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-11-1-111-1-1111-1-1-11
χ16111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-11111-1-1-111-1-111-1-1-1111-1
χ17222222-12222-1-1-1-1-1-1-12222-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-1-100000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-1-1-1-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-21111111100000000000000
χ19222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-122-2-22-21111-1-1-1-111112-2-2-1-1-1-1111100000000000000
χ20222222-12222-1-1-1-1-1-1-122-2-2-1-1-1-1-2-2-2-22-21111-1-1-1-11111-2221111-1-1-1-100000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-122-2-2-2211111111-1-1-1-1-22-2-1-111-1-11100000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-222-1-1-1-1-2-2-2-2-2211111111-1-1-1-12-2211-1-111-1-100000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-12222-2-2-1-1-1-111111111-2-22-1-11111-1-100000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-2-222-2-2-1-1-1-11111111122-211-1-1-1-11100000000000000
χ252222-2-222-22-22-2-22-2-2200222-22-200000-20000000022-2-200000000000002200-2-2000000
χ262222-2-222-22-22-2-22-2-2200222-22-200000-20000000022-2-20000000000000-2-20022000000
χ272222-2-222-22-22-2-22-2-2200-2-22-22-200000200000000-2-22200000000000002-200-22000000
χ282222-2-222-22-22-2-22-2-2200-2-22-22-200000200000000-2-2220000000000000-22002-2000000
χ292222-2-22-22-222-2-22-2-222200-22-220000-20000022-2-20000000000000002200-2-200000000
χ302222-2-22-22-222-2-22-2-222200-22-220000-20000022-2-2000000000000000-2-2002200000000
χ312222-2-22-22-222-2-22-2-22-2-200-22-220000200000-2-2220000000000000002-200-2200000000
χ322222-2-22-22-222-2-22-2-22-2-200-22-220000200000-2-222000000000000000-22002-200000000
χ332-2-222-2222-2-2-2222-2-2-2000022-2-22-200000000000000000002-2000000000000002i−2i2i−2i00
χ342-2-222-2222-2-2-2222-2-2-2000022-2-22-200000000000000000002-200000000000000−2i2i−2i2i00
χ352-2-222-2222-2-2-2222-2-2-2000022-2-2-220000000000000000000-22000000000000002i−2i−2i2i00
χ362-2-222-2222-2-2-2222-2-2-2000022-2-2-220000000000000000000-2200000000000000−2i2i2i−2i00
χ374444444-4-4-4-444444440000-4-4-4-40000000000000000000000000000000000000000000
χ38444444-2-4-4-4-4-2-2-2-2-2-2-200002222000000−2i3−2i32i32i3000000000000000000000000000000000
χ39444444-2-4-4-4-4-2-2-2-2-2-2-2000022220000002i32i3−2i3−2i3000000000000000000000000000000000
χ404444-4-4-24-44-4-222-222-20044-22-2200000-400000000-2-2220000000000000000000000000
χ414444-4-4-24-44-4-222-222-200-4-4-22-220000040000000022-2-20000000000000000000000000
χ424444-4-4-2-44-44-222-222-244002-22-20000-400000-2-22200000000000000000000000000000
χ434444-4-4-2-44-44-222-222-2-4-4002-22-2000040000022-2-200000000000000000000000000000
χ444-44-40040000-400-400422−2222−220000002-2002-22-222−220022−22000000000000000000000000000
χ454-44-40040000-400-400422−22−2222000000-2200-22-2222−2200−2222000000000000000000000000000
χ464-44-40040000-400-4004−222222−22000000-2200-22-22−22220022−22000000000000000000000000000
χ474-44-40040000-400-4004−2222−22220000002-2002-22-2−222200−2222000000000000000000000000000
χ484-44-400-200002−2i32i32−2i32i3-222−2222−220000002-200−1−i31+i3−1+i31−i3−22i6−i6−22i6−i60000000000000000000000000
χ494-44-400-200002−2i32i32−2i32i3-222−22−2222000000-22001+i3−1−i31−i3−1+i3−22i6−i62−2−i6i60000000000000000000000000
χ504-44-400-200002−2i32i32−2i32i3-2−222222−22000000-22001+i3−1−i31−i3−1+i32−2−i6i6−22i6−i60000000000000000000000000
χ514-44-400-200002−2i32i32−2i32i3-2−2222−22220000002-200−1−i31+i3−1+i31−i32−2−i6i62−2−i6i60000000000000000000000000
χ524-44-400-2000022i3−2i322i3−2i3-222−2222−220000002-200−1+i31−i3−1−i31+i3−22−i6i6−22−i6i60000000000000000000000000
χ534-44-400-2000022i3−2i322i3−2i3-222−22−2222000000-22001−i3−1+i31+i3−1−i3−22−i6i62−2i6−i60000000000000000000000000
χ544-44-400-2000022i3−2i322i3−2i3-2−222222−22000000-22001−i3−1+i31+i3−1−i32−2i6−i6−22−i6i60000000000000000000000000
χ554-44-400-2000022i3−2i322i3−2i3-2−2222−22220000002-200−1+i31−i3−1−i31+i32−2i6−i62−2i6−i60000000000000000000000000
χ564-4-444-44-4-444-4444-4-4-40000-4-4440000000000000000000000000000000000000000000
χ574-4-444-4-244-4-42-2-2-22220000-2-2224-40000000000000000000-2200000000000000000000
χ584-4-444-4-244-4-42-2-2-22220000-2-222-4400000000000000000002-200000000000000000000
χ594-4-444-4-2-4-4442-2-2-2222000022-2-200000000000000000000000000023−2300000000000000
χ604-4-444-4-2-4-4442-2-2-2222000022-2-2000000000000000000000000000−232300000000000000
χ614-4-44-4444-4-44-4-4-4444-400004-4-440000000000000000000000000000000000000000000
χ624-4-44-444-444-4-4-4-4444-40000-444-40000000000000000000000000000000000000000000
χ634-4-44-44-24-4-44222-2-2-220000-222-2000000000000000000000000023−230000000000000000
χ644-4-44-44-24-4-44222-2-2-220000-222-20000000000000000000000000−23230000000000000000
χ654-4-44-44-2-444-4222-2-2-2200002-2-220000000000000000000000023−23000000000000000000
χ664-4-44-44-2-444-4222-2-2-2200002-2-2200000000000000000000000−2323000000000000000000
χ6788-8-80080000800-800-8000000000000000000000000000000000000000000000000000
χ6888-8-800-40000-4−4i34i344i3−4i34000000000000000000000000000000000000000000000000000
χ6988-8-800-40000-44i3−4i34−4i34i34000000000000000000000000000000000000000000000000000

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