Finite Group Databasebeta

← Group #11721137

Character table — Group #11721137

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76
size112266661212181818181818181818112266661212181818181818181818112266661212181818181818181818112266661212181818181818181818
order123633663622466661212441212121212121212444121212121212226666666622466661212441212121212121212444121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111-1-111-1-1-1-111111111111-1-111-1-1-1-111111111111-1-111-1-1-1-111111111111-1-111-1-1-1-1
χ31111111111-11-1-1-111-1-11111111111-11-1-1-111-1-11111111111-11-1-1-111-1-11111111111-11-1-1-111-1-1
χ41111111111-1-11-1-1-1-1111111111111-1-11-1-1-1-1111111111111-1-11-1-1-1-1111111111111-1-11-1-1-1-111
χ522222-12-1-1-102000-1-10022222-12-1-1-102000-1-10022222-12-1-1-102000-1-10022222-12-1-1-102000-1-100
χ622222-12-1-1-10-2000110022222-12-1-1-10-2000110022222-12-1-1-10-2000110022222-12-1-1-10-20001100
χ72222-12-12-1-1200-1-100002222-12-12-1-1200-1-100002222-12-12-1-1200-1-100002222-12-12-1-1200-1-10000
χ82222-12-12-1-1-2001100002222-12-12-1-1-2001100002222-12-12-1-1-2001100002222-12-12-1-1-200110000
χ92-22-222-2-22-20000000002-22-222-2-22-20000000002-22-222-2-22-20000000002-22-222-2-22-2000000000
χ102-22-22-1-21-1100000−i3i3002-22-22-1-21-1100000−i3i3002-22-22-1-21-1100000−i3i3002-22-22-1-21-1100000−i3i300
χ112-22-22-1-21-1100000i3−i3002-22-22-1-21-1100000i3−i3002-22-22-1-21-1100000i3−i3002-22-22-1-21-1100000i3−i300
χ122-22-2-121-2-11000−i3i300002-22-2-121-2-11000−i3i300002-22-2-121-2-11000−i3i300002-22-2-121-2-11000−i3i30000
χ132-22-2-121-2-11000i3−i300002-22-2-121-2-11000i3−i300002-22-2-121-2-11000i3−i300002-22-2-121-2-11000i3−i30000
χ144444-2-2-2-2110000000004444-2-2-2-2110000000004444-2-2-2-2110000000004444-2-2-2-211000000000
χ154-44-4-2-2221-10000000004-44-4-2-2221-10000000004-44-4-2-2221-10000000004-44-4-2-2221-1000000000
χ1666-3-30000000020000-1-166-3-30000000020000-1-166-3-30000000020000-1-166-3-30000000020000-1-1
χ1766-3-300000000-200001166-3-300000000-200001166-3-300000000-200001166-3-300000000-2000011
χ186-6-3300000000000003−36-6-3300000000000003−36-6-3300000000000003−36-6-3300000000000003−3
χ196-6-330000000000000−336-6-330000000000000−336-6-330000000000000−336-6-330000000000000−33
χ201111111111111111111iiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ2111111111111-1-111-1-1-1-1iiiiiiiiiii−i−iii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−i−i−i−i−i−i−i−i−i−iii−i−iiiii
χ221111111111-11-1-1-111-1-1iiiiiiiiii−ii−i−i−iii−i−i-1-1-1-1-1-1-1-1-1-11-1111-1-111−i−i−i−i−i−i−i−i−i−ii−iiii−i−iii
χ231111111111-1-11-1-1-1-111iiiiiiiiii−i−ii−i−i−i−iii-1-1-1-1-1-1-1-1-1-111-11111-1-1−i−i−i−i−i−i−i−i−i−iii−iiiii−i−i
χ2422222-12-1-1-102000-1-1002i2i2i2i2i−i2i−i−i−i02i000−i−i00-2-2-2-2-21-21110-20001100−2i−2i−2i−2i−2ii−2iiii0−2i000ii00
χ2522222-12-1-1-10-200011002i2i2i2i2i−i2i−i−i−i0−2i000ii00-2-2-2-2-21-211102000-1-100−2i−2i−2i−2i−2ii−2iiii02i000−i−i00
χ262222-12-12-1-1200-1-100002i2i2i2i−i2i−i2i−i−i2i00−i−i0000-2-2-2-21-21-211-200110000−2i−2i−2i−2ii−2ii−2iii−2i00ii0000
χ272222-12-12-1-1-2001100002i2i2i2i−i2i−i2i−i−i−2i00ii0000-2-2-2-21-21-211200-1-10000−2i−2i−2i−2ii−2ii−2iii2i00−i−i0000
χ282-22-222-2-22-20000000002i−2i2i−2i2i2i−2i−2i2i−2i000000000-22-22-2-222-22000000000−2i2i−2i2i−2i−2i2i2i−2i2i000000000
χ292-22-22-1-21-1100000−i3i3002i−2i2i−2i2i−i−2ii−ii000003−300-22-22-212-11-100000i3−i300−2i2i−2i2i−2ii2i−ii−i00000−3300
χ302-22-22-1-21-1100000i3−i3002i−2i2i−2i2i−i−2ii−ii00000−3300-22-22-212-11-100000−i3i300−2i2i−2i2i−2ii2i−ii−i000003−300
χ312-22-2-121-2-11000−i3i300002i−2i2i−2i−i2ii−2i−ii0003−30000-22-221-2-121-1000i3−i30000−2i2i−2i2ii−2i−i2ii−i000−330000
χ322-22-2-121-2-11000i3−i300002i−2i2i−2i−i2ii−2i−ii000−330000-22-221-2-121-1000−i3i30000−2i2i−2i2ii−2i−i2ii−i0003−30000
χ334444-2-2-2-2110000000004i4i4i4i−2i−2i−2i−2iii000000000-4-4-4-42222-1-1000000000−4i−4i−4i−4i2i2i2i2i−i−i000000000
χ344-44-4-2-2221-10000000004i−4i4i−4i−2i−2i2i2ii−i000000000-44-4422-2-2-11000000000−4i4i−4i4i2i2i−2i−2i−ii000000000
χ3566-3-30000000020000-1-16i6i−3i−3i000000002i0000−i−i-6-63300000000-2000011−6i−6i3i3i00000000−2i0000ii
χ3666-3-300000000-20000116i6i−3i−3i00000000−2i0000ii-6-6330000000020000-1-1−6i−6i3i3i000000002i0000−i−i
χ376-6-3300000000000003−36i−6i−3i3i0000000000000i3−i3-663-30000000000000−33−6i6i3i−3i0000000000000−i3i3
χ386-6-330000000000000−336i−6i−3i3i0000000000000−i3i3-663-300000000000003−3−6i6i3i−3i0000000000000i3−i3
χ391111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4011111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ411111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1111111111111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111
χ421111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11111-1-11111111111-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-111-11111-1-1
χ4322222-12-1-1-102000-1-100-2-2-2-2-21-21110-2000110022222-12-1-1-102000-1-100-2-2-2-2-21-21110-20001100
χ4422222-12-1-1-10-20001100-2-2-2-2-21-211102000-1-10022222-12-1-1-10-20001100-2-2-2-2-21-211102000-1-100
χ452222-12-12-1-1200-1-10000-2-2-2-21-21-211-2001100002222-12-12-1-1200-1-10000-2-2-2-21-21-211-200110000
χ462222-12-12-1-1-200110000-2-2-2-21-21-211200-1-100002222-12-12-1-1-200110000-2-2-2-21-21-211200-1-10000
χ472-22-222-2-22-2000000000-22-22-2-222-220000000002-22-222-2-22-2000000000-22-22-2-222-22000000000
χ482-22-22-1-21-1100000−i3i300-22-22-212-11-100000i3−i3002-22-22-1-21-1100000−i3i300-22-22-212-11-100000i3−i300
χ492-22-22-1-21-1100000i3−i300-22-22-212-11-100000−i3i3002-22-22-1-21-1100000i3−i300-22-22-212-11-100000−i3i300
χ502-22-2-121-2-11000−i3i30000-22-221-2-121-1000i3−i300002-22-2-121-2-11000−i3i30000-22-221-2-121-1000i3−i30000
χ512-22-2-121-2-11000i3−i30000-22-221-2-121-1000−i3i300002-22-2-121-2-11000i3−i30000-22-221-2-121-1000−i3i30000
χ524444-2-2-2-211000000000-4-4-4-42222-1-10000000004444-2-2-2-211000000000-4-4-4-42222-1-1000000000
χ534-44-4-2-2221-1000000000-44-4422-2-2-110000000004-44-4-2-2221-1000000000-44-4422-2-2-11000000000
χ5466-3-30000000020000-1-1-6-63300000000-200001166-3-30000000020000-1-1-6-63300000000-2000011
χ5566-3-300000000-2000011-6-6330000000020000-1-166-3-300000000-2000011-6-6330000000020000-1-1
χ566-6-3300000000000003−3-663-30000000000000−336-6-3300000000000003−3-663-30000000000000−33
χ576-6-330000000000000−33-663-300000000000003−36-6-330000000000000−33-663-300000000000003−3
χ581111111111111111111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiiiiiiiiiiiiii
χ5911111111111-1-111-1-1-1-1−i−i−i−i−i−i−i−i−i−i−iii−i−iiiii-1-1-1-1-1-1-1-1-1-1-111-1-11111iiiiiiiiiii−i−iii−i−i−i−i
χ601111111111-11-1-1-111-1-1−i−i−i−i−i−i−i−i−i−ii−iiii−i−iii-1-1-1-1-1-1-1-1-1-11-1111-1-111iiiiiiiiii−ii−i−i−iii−i−i
χ611111111111-1-11-1-1-1-111−i−i−i−i−i−i−i−i−i−iii−iiiii−i−i-1-1-1-1-1-1-1-1-1-111-11111-1-1iiiiiiiiii−i−ii−i−i−i−iii
χ6222222-12-1-1-102000-1-100−2i−2i−2i−2i−2ii−2iiii0−2i000ii00-2-2-2-2-21-21110-200011002i2i2i2i2i−i2i−i−i−i02i000−i−i00
χ6322222-12-1-1-10-20001100−2i−2i−2i−2i−2ii−2iiii02i000−i−i00-2-2-2-2-21-211102000-1-1002i2i2i2i2i−i2i−i−i−i0−2i000ii00
χ642222-12-12-1-1200-1-10000−2i−2i−2i−2ii−2ii−2iii−2i00ii0000-2-2-2-21-21-211-2001100002i2i2i2i−i2i−i2i−i−i2i00−i−i0000
χ652222-12-12-1-1-200110000−2i−2i−2i−2ii−2ii−2iii2i00−i−i0000-2-2-2-21-21-211200-1-100002i2i2i2i−i2i−i2i−i−i−2i00ii0000
χ662-22-222-2-22-2000000000−2i2i−2i2i−2i−2i2i2i−2i2i000000000-22-22-2-222-220000000002i−2i2i−2i2i2i−2i−2i2i−2i000000000
χ672-22-22-1-21-1100000−i3i300−2i2i−2i2i−2ii2i−ii−i00000−3300-22-22-212-11-100000i3−i3002i−2i2i−2i2i−i−2ii−ii000003−300
χ682-22-22-1-21-1100000i3−i300−2i2i−2i2i−2ii2i−ii−i000003−300-22-22-212-11-100000−i3i3002i−2i2i−2i2i−i−2ii−ii00000−3300
χ692-22-2-121-2-11000−i3i30000−2i2i−2i2ii−2i−i2ii−i000−330000-22-221-2-121-1000i3−i300002i−2i2i−2i−i2ii−2i−ii0003−30000
χ702-22-2-121-2-11000i3−i30000−2i2i−2i2ii−2i−i2ii−i0003−30000-22-221-2-121-1000−i3i300002i−2i2i−2i−i2ii−2i−ii000−330000
χ714444-2-2-2-211000000000−4i−4i−4i−4i2i2i2i2i−i−i000000000-4-4-4-42222-1-10000000004i4i4i4i−2i−2i−2i−2iii000000000
χ724-44-4-2-2221-1000000000−4i4i−4i4i2i2i−2i−2i−ii000000000-44-4422-2-2-110000000004i−4i4i−4i−2i−2i2i2ii−i000000000
χ7366-3-30000000020000-1-1−6i−6i3i3i00000000−2i0000ii-6-63300000000-20000116i6i−3i−3i000000002i0000−i−i
χ7466-3-300000000-2000011−6i−6i3i3i000000002i0000−i−i-6-6330000000020000-1-16i6i−3i−3i00000000−2i0000ii
χ756-6-3300000000000003−3−6i6i3i−3i0000000000000−i3i3-663-30000000000000−336i−6i−3i3i0000000000000i3−i3
χ766-6-330000000000000−33−6i6i3i−3i0000000000000i3−i3-663-300000000000003−36i−6i−3i3i0000000000000−i3i3

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