Finite Group Databasebeta

← Group #114513

Character table — Group #114513

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12222222222244444444444444444422224444888888888888888888888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ9111111111111111-1-1-1-1-1-1-1-11-1-1-111-11111-1-1-1-1iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i
χ10111111111111111-1-1-1-1-1-1-1-11-1-1-111-11111-1-1-1-1iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii-1-111ii−i−i−i−iii
χ11111111111111111-1-1-1-1-1-1-1-11-1-1-111-11111-1-1-1-1−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii
χ12111111111111111-1-1-1-1-1-1-1-11-1-1-111-11111-1-1-1-1−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i-1-111−i−iiiii−i−i
χ13111111111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−i−iii−i−iii
χ14111111111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-11111iiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii11-1-1−i−iiiii−i−i
χ15111111111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii-1-111ii−i−iii−i−i
χ16111111111111111-1-1-1-1-1-1-1-11-1-1-111-1-1-1-1-11111−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i11-1-1ii−i−i−i−iii
χ17222222222222-2-2-222222222-2-2-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ18222222222222-2-2-222222222-2-2-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ19222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ20222222222222-2-2-2-2-2-2-2-2-2-2-2-2222-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ2122222222-2-2-2-22222222-2-2-2-222-2-2-2-2222-2-222-2-2000000000000000000000000000000000000
χ2222222222-2-2-2-22222222-2-2-2-222-2-2-2-22-2-222-2-222000000000000000000000000000000000000
χ2322222222-2-2-2-2222-2-2-2-222222-222-2-2-222-2-2-2-222000000000000000000000000000000000000
χ2422222222-2-2-2-2222-2-2-2-222222-222-2-2-2-2-22222-2-2000000000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-2-2-2-22222-20000000000000000000000000000000000002i−2i2i−2i0000
χ2622222222-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2000000000000000000000000000000000000−2i2i−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-22-2-22220000000000000000000000000000000000002-2-220000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-22-2-2222000000000000000000000000000000000000-222-20000
χ29222-2-22-2-222-2-20002i−2i2i−2i2i2i−2i−2i000000000000000002ζ3−2ζ3002ζ−2ζ22−2−2i2i2−i2−i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ30222-2-22-2-222-2-20002i−2i2i−2i2i2i−2i−2i000000000000000002ζ3−2ζ3002ζ−2ζ−2−222−i2−i2i2i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ31222-2-22-2-222-2-20002i−2i2i−2i2i2i−2i−2i00000000000000000−2ζ32ζ300−2ζ2ζ22−2−2i2i2−i2−i2−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000
χ32222-2-22-2-222-2-20002i−2i2i−2i2i2i−2i−2i00000000000000000−2ζ32ζ300−2ζ2ζ−2−222−i2−i2i2i21−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000
χ33222-2-22-2-222-2-2000−2i2i−2i2i−2i−2i2i2i000000000000000002ζ−2ζ002ζ3−2ζ322−2−2−i2−i2i2i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ34222-2-22-2-222-2-2000−2i2i−2i2i−2i−2i2i2i000000000000000002ζ−2ζ002ζ3−2ζ3−2−222i2i2−i2−i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ35222-2-22-2-222-2-2000−2i2i−2i2i−2i−2i2i2i00000000000000000−2ζ2ζ00−2ζ32ζ322−2−2−i2−i2i2i21+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000
χ36222-2-22-2-222-2-2000−2i2i−2i2i−2i−2i2i2i00000000000000000−2ζ2ζ00−2ζ32ζ3−2−222i2i2−i2−i2−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000
χ372-2-2222-2-22-22-20002i−2i−2i2i2i−2i2i−2i0000000000000002ζ−2ζ002ζ3−2ζ3002−22−2i2−i2i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ382-2-2222-2-22-22-20002i−2i−2i2i2i−2i2i−2i0000000000000002ζ−2ζ002ζ3−2ζ300−22−22−i2i2−i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ392-2-2222-2-22-22-20002i−2i−2i2i2i−2i2i−2i000000000000000−2ζ2ζ00−2ζ32ζ3002−22−2i2−i2i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ402-2-2222-2-22-22-20002i−2i−2i2i2i−2i2i−2i000000000000000−2ζ2ζ00−2ζ32ζ300−22−22−i2i2−i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ412-2-2222-2-22-22-2000−2i2i2i−2i−2i2i−2i2i0000000000000002ζ3−2ζ3002ζ−2ζ002−22−2−i2i2−i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ422-2-2222-2-22-22-2000−2i2i2i−2i−2i2i−2i2i0000000000000002ζ3−2ζ3002ζ−2ζ00−22−22i2−i2i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ432-2-2222-2-22-22-2000−2i2i2i−2i−2i2i−2i2i000000000000000−2ζ32ζ300−2ζ2ζ002−22−2−i2i2−i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ442-2-2222-2-22-22-2000−2i2i2i−2i−2i2i−2i2i000000000000000−2ζ32ζ300−2ζ2ζ00−22−22i2−i2i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ452-2-2-2-22222-2-2222-222-2-22-2-22-222-22-2-20000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000
χ462-2-2-2-22222-2-2222-222-2-22-2-22-222-22-2-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000
χ472-2-2-2-22222-2-2222-2-2-222-222-2-2-2-222-220000000000000000000000002-2-222-2-22000000000000
χ482-2-2-2-22222-2-2222-2-2-222-222-2-2-2-222-22000000000000000000000000-222-2-222-2000000000000
χ492-2-2-2-22222-2-22-2-2222-2-22-2-222-2-22-22200000000000000002-2-222-2-2200000000000000000000
χ502-2-2-2-22222-2-22-2-2222-2-22-2-222-2-22-2220000000000000000-222-2-222-200000000000000000000
χ512-2-2-2-22222-2-22-2-22-2-222-222-2222-2-22-200000000000000002-2-22-222-200000000000000000000
χ522-2-2-2-22222-2-22-2-22-2-222-222-2222-2-22-20000000000000000-222-22-2-2200000000000000000000
χ532-2-2-2-2222-222-222-222-2-2-222-2-22-22-22-200000000000000000000000000000000000000002i−2i2i−2i
χ542-2-2-2-2222-222-222-222-2-2-222-2-22-22-22-20000000000000000000000000000000000000000−2i2i−2i2i
χ552-2-2-2-2222-222-222-2-2-2222-2-22-2-22-2-22200000000000000000000000000000000000000002-2-22
χ562-2-2-2-2222-222-222-2-2-2222-2-22-2-22-2-2220000000000000000000000000000000000000000-222-2
χ572-2-2-2-2222-222-2-2-2222-2-2-222-22-22-22-22000000000000000000000000000000002-22-200000000
χ582-2-2-2-2222-222-2-2-2222-2-2-222-22-22-22-2200000000000000000000000000000000-22-2200000000
χ592-2-2-2-2222-222-2-2-22-2-2222-2-2222-222-2-2000000000000000000000000000000002-2-2200000000
χ602-2-2-2-2222-222-2-2-22-2-2222-2-2222-222-2-200000000000000000000000000000000-222-200000000
χ61444-4-44-4-4-4-4440004i−4i4i−4i−4i−4i4i4i000000000000000000000000000000000000000000000000000
χ62444-4-44-4-4-4-444000−4i4i−4i4i4i4i−4i−4i000000000000000000000000000000000000000000000000000
χ6344-44-4-44-400004-4400000000-40000000000004i−4i000000000000000000000000000000000000
χ6444-44-4-44-400004-4400000000-4000000000000−4i4i000000000000000000000000000000000000
χ6544-44-4-44-40000-44-40000000040000004-4000000000000000000000000000000000000000000
χ6644-44-4-44-40000-44-4000000004000000-44000000000000000000000000000000000000000000
χ674-44-44-44-400004-4-4000000004000000004-40000000000000000000000000000000000000000
χ684-44-44-44-400004-4-400000000400000000-440000000000000000000000000000000000000000
χ694-44-44-44-40000-44400000000-400000000004i−4i00000000000000000000000000000000000000
χ704-44-44-44-40000-44400000000-40000000000−4i4i00000000000000000000000000000000000000
χ714-4-4444-4-4-44-440004i−4i−4i4i−4i4i−4i4i000000000000000000000000000000000000000000000000000
χ724-4-4444-4-4-44-44000−4i4i4i−4i4i−4i4i−4i000000000000000000000000000000000000000000000000000
χ7388-8-88-8-88000000000000000000000000000000000000000000000000000000000000000000
χ748-888-8-8-88000000000000000000000000000000000000000000000000000000000000000000

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