Finite Group Databasebeta

← Group #72339091

Character table — Group #72339091

Order 4096.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67
size11244488161616161616161616161616161616163232323232323232323232646464646464646464646464646464646464128128128128128128128128128128256256256256
order1222224422222222224444442244444888824444444888888888844444488888888
χ11111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1111-1-11-1-111111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ51111111111111-1-1-1-11111111111-1-1111111111-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ61111111111111-1-1-1-11111111111-1-1111111111-1-111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-111
χ71111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111
χ81111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-11111-1-1-1-111111111-1-1
χ911111111111-1-111-1-1111-1-1-1-1-1-1-11-1111111-1-111-1-1-1-111ii−i−iii−i−i1-1i−ii−iii−i−i1-1i−i
χ1011111111111-1-111-1-1111-1-1-1-1-1-1-11-1111111-1-111-1-1-1-111−i−iii−i−iii1-1−ii−ii−i−iii1-1−ii
χ1111111111111-1-111-1-1111-1-1-1-1-1-1-11-111-1-1-1-11111-111-1-1-1ii−i−iii−i−i1-1i−ii−i−i−iii-11−ii
χ1211111111111-1-111-1-1111-1-1-1-1-1-1-11-111-1-1-1-11111-111-1-1-1−i−iii−i−iii1-1−ii−iiii−i−i-11i−i
χ1311111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-11-11-1-1-111ii−i−i−i−iii-11i−i−iiii−i−i-11−ii
χ1411111111111-1-1-1-111111-1-1-1-1-1-1-1-11111111-1-11-11-1-1-111−i−iiiii−i−i-11−iii−i−i−iii-11i−i
χ1511111111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1111-1-1-1ii−i−i−i−iii-11i−i−ii−i−iii1-1i−i
χ1611111111111-1-1-1-111111-1-1-1-1-1-1-1-1111-1-1-1-1111-1111-1-1-1−i−iiiii−i−i-11−iii−iii−i−i1-1−ii
χ1722222222222220000222-222-22-2200-2-2000000-20000-20000002i2i−2i−2i0000−2i2i00000000
χ1822222222222220000222-222-22-2200-2-2000000-20000-2000000−2i−2i2i2i00002i−2i00000000
χ1922222222222-2-200002222-2-22-22-200-2-2000000-20000200000022220000-2-200000000
χ2022222222222-2-200002222-2-22-22-200-2-2000000-200002000000-2-2-2-200002200000000
χ21222222222-2-22200002-2-2-2-2-2-2-2-2200-2-2000000200002002i2i−2i−2i000000−2i2i0000000000
χ22222222222-2-22200002-2-2-2-2-2-2-2-2200-2-200000020000200−2i−2i2i2i0000002i−2i0000000000
χ23222222222-2-22222222-2-22-2-22-2222222000000-22200-20000000000-2-2000000000000
χ24222222222-2-222-2-2-2-22-2-22-2-22-222-2-222000000-2-2-200-2000000000022000000000000
χ25222222222-2-2-2-200002-2-2222222-200-2-200000020000-2002222000000-2-20000000000
χ26222222222-2-2-2-200002-2-2222222-200-2-200000020000-200-2-2-2-2000000220000000000
χ27222222222-2-2-2-222-2-22-2-2-222-22-2-22-222000000-22-20020000000000-22000000000000
χ28222222222-2-2-2-2-2-2222-2-2-222-22-2-2-2222000000-2-2200200000000002-2000000000000
χ2944444444-400000000-40040040-4000002222-2-2000220-2-20000000000000000000000
χ3044444444-400000000-40040040-400000-2-2-2-222000-2-20220000000000000000000000
χ3144444444-400000000-400-400-40400000222222000-2-20-2-20000000000000000000000
χ3244444444-400000000-400-400-40400000-2-2-2-2-2-2000220220000000000000000000000
χ33444444-4-4-4000000444000000000044-400000000-4000000000000000000000000000
χ34444444-4-4-4000000-4-440000000000-44-4000000004000000000000000000000000000
χ35444444-4-4-400004400400000000040-440000000-40000000000000000000000000000
χ36444444-4-4-40000-4-4004000000000-40-44000000040000000000000000000000000000
χ37888888-8-8800000000-80000000000000000000000000000000000000000000000000
χ388888-8-8000000000000000440-400000000000000000000000000000000002-22-20000
χ398888-8-8000000000000000440-40000000000000000000000000000000000-22-220000
χ408888-8-8000000000000000-4-40400000000000000000000000000000000002i−2i−2i2i0000
χ418888-8-8000000000000000-4-4040000000000000000000000000000000000−2i2i2i−2i0000
χ42888-88-800000444444000000000-4-4-400000000000000000000000000000000000000
χ43888-88-80000044-4-4-4-4000000000-44400000000000000000000000000000000000000
χ44888-88-800000-4-444-4-40000000004-4400000000000000000000000000000000000000
χ45888-88-800000-4-4-4-44400000000044-400000000000000000000000000000000000000
χ46888-8-88000440000000-4-4000000000000000000000004-40000000000000000000000
χ47888-8-88000440000000-4-400000000000000000000000-440000000000000000000000
χ48888-8-88000-4-40000000440000000000044-4-400000000000000000000000000000000
χ49888-8-88000-4-400000004400000000000-4-44400000000000000000000000000000000
χ5088-8000-440004-4000004-404-400000000004-42-20002-20000000000000000000000000
χ5188-8000-440004-4000004-404-40000000000-44-22000-220000000000000000000000000
χ5288-8000-440004-400000-440-44000000004-4002-2000-220000000000000000000000000
χ5388-8000-440004-400000-440-4400000000-4400-220002-20000000000000000000000000
χ5488-8000-44000-44000004-40-4400000000004-4-22000-220000000000000000000000000
χ5588-8000-44000-44000004-40-440000000000-442-20002-20000000000000000000000000
χ5688-8000-44000-4400000-4404-4000000004-400-220002-20000000000000000000000000
χ5788-8000-44000-4400000-4404-400000000-44002-2000-220000000000000000000000000
χ581616-160008-808-800000000000000000000000000000000000000000000000000000000
χ591616-160008-80-8800000000000000000000000000000000000000000000000000000000
χ6016-16000000000004-44-4000400-40000000000000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ6116-16000000000004-44-4000400-4000000000000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ6216-16000000000004-4-44000-40040000000000000000000002-2-222-2-2200000000000000
χ6316-16000000000004-4-44000-4004000000000000000000000-222-2-222-200000000000000
χ6416-1600000000000-444-4000-40040000000000000000000002-2-22-222-200000000000000
χ6516-1600000000000-444-4000-4004000000000000000000000-222-22-2-2200000000000000
χ6616-1600000000000-44-44000400-40000000000000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ6716-1600000000000-44-44000400-4000000000000000000000−2i2i−2i2i2i−2i2i−2i00000000000000

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