Finite Group Databasebeta

← Group #99048

Character table — Group #99048

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12222222444444444444444444448888888888888888224488888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ911111111-1-1-1-1-1111-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1ii−i−iii−i−i11-1-1ii−i−iii−i−i
χ1011111111-1-1-1-1-1111-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1−i−iii−i−iii11-1-1−i−iii−i−iii
χ1111111111-1-1-1-1-1111-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11ii−i−iii−i−i-1-111−i−iii−i−iii
χ1211111111-1-1-1-1-1111-1-11-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11−i−iii−i−iii-1-111ii−i−iii−i−i
χ1311111111-1-1-1-1-1111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1ii−i−i−i−iii-1-111ii−i−i−i−iii
χ1411111111-1-1-1-1-1111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1−i−iiiii−i−i-1-111−i−iiiii−i−i
χ1511111111-1-1-1-1-1111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11ii−i−i−i−iii11-1-1−i−iiiii−i−i
χ1611111111-1-1-1-1-1111-1-11-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11−i−iiiii−i−i11-1-1ii−i−i−i−iii
χ172222222222222-2-2-222-2222-2-2-2-2-2-2000000000000000022-2-200000000000000000000
χ182222222222222-2-2-222-2222-2-2-2-2-2-20000000000000000-2-22200000000000000000000
χ1922222222222-2-2222-2-222-2-2-2-222-2-22222-2-2-2-22222-2-2-2-2000000000000000000000000
χ2022222222222-2-2222-2-222-2-2-2-222-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000
χ2122222222222-2-2-2-2-2-2-2-22-2-222-2-22200000000000000000000000000002i−2i2i−2i00000000
χ2222222222222-2-2-2-2-2-2-2-22-2-222-2-2220000000000000000000000000000−2i2i−2i2i00000000
χ2322222222-2-2-222222222-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222000000000000000000000000
χ2422222222-2-2-222222222-2-2-2-2-2-2-222-2-2-2-222222222-2-2-2-2000000000000000000000000
χ2522222222-2-2-222-2-2-222-2-2-2-22222-2-200000000000000000000000000002i−2i−2i2i00000000
χ2622222222-2-2-222-2-2-222-2-2-2-22222-2-20000000000000000000000000000−2i2i2i−2i00000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000000000002-2-2200000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000000000000000-222-200000000000000000000
χ29222-2-2-2-220002-222-22-2-200000002-22i2i−2i−2i000000002i2i−2i−2i00000000000000002−22−2i2−i2i2−i2
χ30222-2-2-2-220002-222-22-2-200000002-22i2i−2i−2i000000002i2i−2i−2i0000000000000000−22−22−i2i2−i2i2
χ31222-2-2-2-220002-222-22-2-200000002-2−2i−2i2i2i00000000−2i−2i2i2i00000000000000002−22−2−i2i2−i2i2
χ32222-2-2-2-220002-222-22-2-200000002-2−2i−2i2i2i00000000−2i−2i2i2i0000000000000000−22−22i2−i2i2−i2
χ33222-2-2-2-22000-2222-2-22-20000000-222i2i−2i−2i00000000−2i−2i2i2i0000000000000000i2−i2−i2i2−222−2
χ34222-2-2-2-22000-2222-2-22-20000000-222i2i−2i−2i00000000−2i−2i2i2i0000000000000000−i2i2i2−i22−2−22
χ35222-2-2-2-22000-2222-2-22-20000000-22−2i−2i2i2i000000002i2i−2i−2i0000000000000000i2−i2−i2i22−2−22
χ36222-2-2-2-22000-2222-2-22-20000000-22−2i−2i2i2i000000002i2i−2i−2i0000000000000000−i2i2i2−i2−222−2
χ372-2-222-2-2222-2002-2-2002-200002-200000022-2-200002-22-20000i2−i2i2−i2i2−i2i2−i2000000000000
χ382-2-222-2-2222-2002-2-2002-200002-200000022-2-200002-22-20000−i2i2−i2i2−i2i2−i2i2000000000000
χ392-2-222-2-2222-2002-2-2002-200002-2000000-2-2220000-22-220000i2−i2i2−i2−i2i2−i2i2000000000000
χ402-2-222-2-2222-2002-2-2002-200002-2000000-2-2220000-22-220000−i2i2−i2i2i2−i2i2−i2000000000000
χ412-2-222-2-22-2-22002-2-200220000-2200000022-2-20000-22-2200002−2−222−2−22000000000000
χ422-2-222-2-22-2-22002-2-200220000-2200000022-2-20000-22-220000−222−2−222−2000000000000
χ432-2-222-2-22-2-22002-2-200220000-22000000-2-22200002-22-200002−2−22−222−2000000000000
χ442-2-222-2-22-2-22002-2-200220000-22000000-2-22200002-22-20000−222−22−2−22000000000000
χ45444-4-4-4-440004-4-4-444-440000000-440000000000000000000000000000000000000000
χ46444-4-4-4-44000-44-4-44-44400000004-40000000000000000000000000000000000000000
χ4744-44-44-4-4000000000000004i−4i00002i2−2i22i2−2i222−2222−2200000000000000000000000000000000
χ4844-44-44-4-4000000000000004i−4i0000−2i22i2−2i22i2−2222−222200000000000000000000000000000000
χ4944-44-44-4-400000000000000−4i4i00002i2−2i22i2−2i2−2222−222200000000000000000000000000000000
χ5044-44-44-4-400000000000000−4i4i0000−2i22i2−2i22i222−2222−2200000000000000000000000000000000
χ5144-4-44-44-44-4400000000-40000000022−22−222200002222−22−220000000000000000000000000000
χ5244-4-44-44-44-4400000000-400000000−222222−220000−22−2222220000000000000000000000000000
χ5344-4-44-44-4-44-40000000040000000022−22−22220000−22−2222220000000000000000000000000000
χ5444-4-44-44-4-44-400000000400000000−222222−2200002222−22−220000000000000000000000000000
χ554-444-4-44-400044000-4-40000000000000022−22−222222−2222−220000000000000000000000000000
χ564-444-4-44-400044000-4-400000000000000−222222−22−2222−22220000000000000000000000000000
χ574-444-4-44-4000-4-4000440000000000000022−22−2222−2222−22220000000000000000000000000000
χ584-444-4-44-4000-4-40004400000000000000−222222−2222−2222−220000000000000000000000000000
χ594-44-444-4-44-4-44-4000-44044-40000000000000000000000000000000000000000000000
χ604-44-444-4-44-4-4-440004-404-440000000000000000000000000000000000000000000000
χ614-44-444-4-4-4444-4000-440-4-440000000000000000000000000000000000000000000000
χ624-44-444-4-4-444-440004-40-44-40000000000000000000000000000000000000000000000
χ634-4-444-4-4444-400-44400-4-40000-44000000000000000000000000000000000000000000
χ644-4-444-4-44-4-4400-44400-4400004-4000000000000000000000000000000000000000000
χ654-4-4-4-4444000004-4400-40000000000000000000004i−4i−4i4i000000000000000000000000
χ664-4-4-4-4444000004-4400-4000000000000000000000−4i4i4i−4i000000000000000000000000
χ674-4-4-4-444400000-44-4004000000000000000004-4-440000000000000000000000000000
χ684-4-4-4-444400000-44-400400000000000000000-444-40000000000000000000000000000

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