Finite Group Databasebeta

← Group #72342965

Character table — Group #72342965

Order 1024.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size1122222444444444448888888888888161616161616161616161616161616161616161616161616161632323232323264646464
order1224488222444816161616244488816161616161644448816161616323232323232323232323232323232322244444488
χ11111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-111
χ7111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-111
χ8111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111-1-1
χ911111111-1-11-1-11111111-1-11-1-111-1-1-1-11111-1111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-111i−ii−i
χ1011111111-1-11-1-11111111-1-11-1-111-1-1-1-11111-1111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-111−ii−ii
χ1111111111-1-11-1-11111111-1-11-1-111-1-1-1-1-1-1-1-1-1111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1−ii−ii
χ1211111111-1-11-1-11111111-1-11-1-111-1-1-1-1-1-1-1-1-1111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1i−ii−i
χ1311111111-1-11-1-111111-1-1111-1-111-1-1-1-111111-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1i−i−ii
χ1411111111-1-11-1-111111-1-1111-1-111-1-1-1-111111-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1−iii−i
χ1511111111-1-11-1-111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111−iii−i
χ1611111111-1-11-1-111111-1-1111-1-111-1-1-1-1-1-1-1-11-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111i−i−ii
χ1722222222222222-2-2-2-22222222-2-2-2-2-2-2000022-2-2-2-200000000000000000000000000
χ1822222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-20000-2-2222200000000000000000000000000
χ1922222222-2-22-2-22-2-2-2-222-2-22-2-2-2-222220000-22-2-22200000000000000000000000000
χ2022222222-2-22-2-22-2-2-2-2-2-2222-2-2-2-2222200002-222-2-200000000000000000000000000
χ212222222-22-2-2-22222220000-22-2-2-222-2-222-2-20000000000000000000000002-2000000
χ222222222-22-2-2-22222220000-22-2-2-222-2-2-2-222000000000000000000000000-22000000
χ232222222-22-2-2-222-2-2-2-20000-22-222-2-222000000000000000000000000002-2002-20000
χ242222222-22-2-2-222-2-2-2-20000-22-222-2-22200000000000000000000000000-2200-220000
χ252222222-2-22-22-2222220000-2-22-2-2-2-22222-2-2000000000000000000000000-22000000
χ262222222-2-22-22-2222220000-2-22-2-2-2-222-2-2220000000000000000000000002-2000000
χ272222222-2-22-22-22-2-2-2-20000-2-222222-2-2000000000000000000000000002-200-220000
χ282222222-2-22-22-22-2-2-2-20000-2-222222-2-200000000000000000000000000-22002-20000
χ2922222-2-2222222-200002222-2-2-20000000000-2-2000022−2−222−2−222−2−222−2−20000000000
χ3022222-2-2222222-200002222-2-2-20000000000-2-20000−2−222−2−222−2−222−2−2220000000000
χ3122222-2-2222222-20000-2-2-2-2-2-2-2000000000022000022−2−222−2−2−2−222−2−2220000000000
χ3222222-2-2222222-20000-2-2-2-2-2-2-20000000000220000−2−222−2−22222−2−222−2−20000000000
χ3322222-2-22-2-22-2-2-2000022-2-2-22200000000002-20000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000000000
χ3422222-2-22-2-22-2-2-2000022-2-2-22200000000002-20000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000000000
χ3522222-2-22-2-22-2-2-20000-2-222-2220000000000-220000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000000000
χ3622222-2-22-2-22-2-2-20000-2-222-2220000000000-220000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000000000
χ37222-2-20022-2-22-2022−2−22-22-20002−22−22−20000002−22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000
χ38222-2-20022-2-22-2022−2−22-22-20002−22−22−20000002−22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000
χ39222-2-20022-2-22-2022−2−2-22-220002−22−22−2000000−22−22ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000000000
χ40222-2-20022-2-22-2022−2−2-22-220002−22−22−2000000−22−22−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000000000
χ41222-2-20022-2-22-20−2−2222-22-2000−22−22−22000000−22−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000
χ42222-2-20022-2-22-20−2−2222-22-2000−22−22−22000000−22−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000
χ43222-2-20022-2-22-20−2−222-22-22000−22−22−220000002−22−2ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000000000
χ44222-2-20022-2-22-20−2−222-22-22000−22−22−220000002−22−2−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000000000
χ45222-2-2002-22-2-22022−2−22-2-220002−2−22−220000002−2−22ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ46222-2-2002-22-2-22022−2−22-2-220002−2−22−220000002−2−22−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ47222-2-2002-22-2-22022−2−2-222-20002−2−22−22000000−222−2ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000000000
χ48222-2-2002-22-2-22022−2−2-222-20002−2−22−22000000−222−2−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000000000
χ49222-2-2002-22-2-220−2−2222-2-22000−222−22−2000000−222−2ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ50222-2-2002-22-2-220−2−2222-2-22000−222−22−2000000−222−2−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ51222-2-2002-22-2-220−2−222-222-2000−222−22−20000002−2−22ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000000000
χ52222-2-2002-22-2-220−2−222-222-2000−222−22−20000002−2−22−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000000000
χ5344444-4-4-44-4-4-44-4000000004-44000000000000000000000000000000000000000000
χ5444444-4-4-4-44-44-4-40000000044-4000000000000000000000000000000000000000000
χ55444-4-400-4444-4-402222−22−220000000−222222−22−2222000000000000000000000000000000000000
χ56444-4-400-4444-4-40−22−222222000000022−22−222222−22000000000000000000000000000000000000
χ57444-4-400-4-4-444402222−22−220000000−2222−222222−22000000000000000000000000000000000000
χ58444-4-400-4-4-44440−22−222222000000022−2222−22−2222000000000000000000000000000000000000
χ5944-4-4444000000-44-44-40000000000000004i−4i00000000000000000000000000000000
χ6044-4-4444000000-44-44-4000000000000000−4i4i00000000000000000000000000000000
χ6144-4-4444000000-4-44-4400000000000004i−4i0000000000000000000000000000000000
χ6244-4-4444000000-4-44-440000000000000−4i4i0000000000000000000000000000000000
χ6388-88-800000000042−42−42420000000000000000000000000000000000000000000000000
χ6488-88-8000000000−424242−420000000000000000000000000000000000000000000000000
χ6588-8-88-8-8000000800000000000000000000000000000000000000000000000000000
χ6616-1600082−82000000000000000000000000000000000000000000000000000000000000
χ6716-16000−8282000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.