Finite Group Databasebeta

← Group #100447

Character table — Group #100447

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222222244444444444444222244444888888888888888844448888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ511111111111111111111111111-1-1-1-11-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ1011111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ1111111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ1211111111-1-1-1-111-1-111-1-1-1-111-1-111-1-1111-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ1311111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ1411111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ1511111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ1611111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1111-1-111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ1722222222222222-2-222-2-2-2-2-2-2222222-2-2-2-2-2000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-222-2-2-2-2-22222000000000000000000000000000000
χ19222222222222-2-222-2-222-2-222-2-20000-200002222-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-222-2-222-2-20000-20000-2-2-2-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-222-2-2-2-20000200000000000000000000000000002i−2i2i−2i00
χ22222222222222-2-2-2-2-2-2-2-222-2-2-2-2000020000000000000000000000000000−2i2i−2i2i00
χ2322222222-2-2-2-22222222222-2-2-2-222-2-2-2-2-222000000000000000000000000000000
χ2422222222-2-2-2-22222222222-2-2-2-2-2-222-222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-2-2-2220000200000000000000000000000000002-2-2200
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-222000020000000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-200002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-22222220000-20000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ29222-2-2-22-200002-22i−2i2-22i−2i2i−2i0000002-202i−2i00000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i−1+i1+i−1−i0000000000
χ30222-2-2-22-200002-22i−2i2-22i−2i2i−2i0000002-202i−2i0000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i1−i−1−i1+i0000000000
χ31222-2-2-22-200002-22i−2i2-22i−2i2i−2i000000-220−2i2i00000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i1−i−1−i1+i0000000000
χ32222-2-2-22-200002-22i−2i2-22i−2i2i−2i000000-220−2i2i0000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i−1+i1+i−1−i0000000000
χ33222-2-2-22-200002-2−2i2i2-2−2i2i−2i2i0000002-20−2i2i00000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i−1−i1−i−1+i0000000000
χ34222-2-2-22-200002-2−2i2i2-2−2i2i−2i2i0000002-20−2i2i0000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i1+i−1+i1−i0000000000
χ35222-2-2-22-200002-2−2i2i2-2−2i2i−2i2i000000-2202i−2i00000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i1+i−1+i1−i0000000000
χ36222-2-2-22-200002-2−2i2i2-2−2i2i−2i2i000000-2202i−2i0000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i−1−i1−i−1+i0000000000
χ3722-22-2-2-2222-2-200-2-20022002-20000000000000002-22-2i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i2000000
χ3822-22-2-2-2222-2-200-2-20022002-20000000000000002-22-2−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i2000000
χ3922-22-2-2-2222-2-200-2-20022002-2000000000000000-22-22i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i2000000
χ4022-22-2-2-2222-2-200-2-20022002-2000000000000000-22-22−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i2000000
χ4122-22-2-2-22-2-222002200-2-2002-20000000000000002i−2i−2i2i2−22−2−22−220000−i2i2i2−i2000000
χ4222-22-2-2-22-2-222002200-2-2002-20000000000000002i−2i−2i2i−22−222−22−20000i2−i2−i2i2000000
χ4322-22-2-2-22-2-222002200-2-2002-2000000000000000−2i2i2i−2i2−22−2−22−220000i2−i2−i2i2000000
χ4422-22-2-2-22-2-222002200-2-2002-2000000000000000−2i2i2i−2i−22−222−22−20000−i2i2i2−i2000000
χ45444-4-4-44-40000-444i−4i-444i−4i−4i4i0000000000000000000000000000000000000000000
χ46444-4-4-44-40000-44−4i4i-44−4i4i4i−4i0000000000000000000000000000000000000000000
χ4744-44-4-4-4444-4-4004400-4-400-4400000000000000000000000000000000000000000
χ4844-44-4-4-44-4-44400-4-4004400-4400000000000000000000000000000000000000000
χ4944-4-444-4-40000004i−4i00−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5044-4-444-4-40000004i−4i00−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5144-4-444-4-4000000−4i4i004i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5244-4-444-4-4000000−4i4i004i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ534-4444-4-4-44-44-40000000000000000000000022−2222−2200000000000000000000000000
χ544-4444-4-4-44-44-400000000000000000000000−2222−222200000000000000000000000000
χ554-4444-4-4-4-44-44000000000000000000000002i2−2i2−2i22i200000000000000000000000000
χ564-4444-4-4-4-44-4400000000000000000000000−2i22i22i2−2i200000000000000000000000000
χ574-4-44-444-44-4-444400-4-4000000-44000000000000000000000000000000000000000
χ584-4-44-444-44-4-44-4-400440000004-4000000000000000000000000000000000000000
χ594-4-44-444-4-444-44400-4-40000004-4000000000000000000000000000000000000000
χ604-4-44-444-4-444-4-4-40044000000-44000000000000000000000000000000000000000
χ614-4-4-44-44400004-400-44000000004-40000000000000000000000000000000000000
χ624-4-4-44-44400004-400-4400000000-440000000000000000000000000000000000000
χ634-4-4-44-4440000-44004-40000000000000004-4000000000000000000000000000000
χ644-4-4-44-4440000-44004-4000000000000000-44000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.