Finite Group Databasebeta

← Group #72220811

Character table — Group #72220811

Order 10368.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1188889999181818183232323272727272727272728181144144144144144144144144144144144144162162162162162162162162162162162162162162162162162162162162162162162162288288288288648648648648
order1233662222444433662244666622666612121212121212124444444488888888888888886612124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ71111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91-111-1-111-1-1ii−i−i11-1-11-1i−i11-1-1-1111-1-1ii−i−iii−i−iii−i−i1-11-1iiii−i−i−i−i1111-1-1-1-11-1i−ii−i1-1
χ101-111-1-111-1-1ii−i−i11-1-11-1i−i11-1-1-1111-1-1ii−i−iii−i−iii−i−i1-11-1−i−i−i−iiiii-1-1-1-111111-1i−i−ii-11
χ111-111-1-111-1-1ii−i−i11-1-1-11−ii11-1-1-11-1-111−i−iiiii−i−iii−i−i1-11-1iiii−i−i−i−i1111-1-1-1-1-11−ii−ii-11
χ121-111-1-111-1-1ii−i−i11-1-1-11−ii11-1-1-11-1-111−i−iiiii−i−iii−i−i1-11-1−i−i−i−iiiii-1-1-1-11111-11−iii−i1-1
χ131-111-1-111-1-1−i−iii11-1-11-1−ii11-1-1-1111-1-1−i−iii−i−iii−i−iii1-11-1iiii−i−i−i−i-1-1-1-111111-1−iii−i-11
χ141-111-1-111-1-1−i−iii11-1-11-1−ii11-1-1-1111-1-1−i−iii−i−iii−i−iii1-11-1−i−i−i−iiiii1111-1-1-1-11-1−ii−ii1-1
χ151-111-1-111-1-1−i−iii11-1-1-11i−i11-1-1-11-1-111ii−i−i−i−iii−i−iii1-11-1iiii−i−i−i−i-1-1-1-11111-11i−i−ii1-1
χ161-111-1-111-1-1−i−iii11-1-1-11i−i11-1-1-11-1-111ii−i−i−i−iii−i−iii1-11-1−i−i−i−iiiii1111-1-1-1-1-11i−ii−i-11
χ1722222222222-22-222220000222222000000002-22-22-22-2-2-2-2-2000000000000000000000000
χ182222222222-22-222222000022222200000000-22-22-22-22-2-2-2-2000000000000000000000000
χ192222222-22-20202222200002-22-2-2-20000000002020-20-20000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ202222222-22-20202222200002-22-2-2-20000000002020-20-20000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ212222222-22-20-20-2222200002-22-2-2-2000000000-20-202020000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ222222222-22-20-20-2222200002-22-2-2-2000000000-20-202020000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ23222222-22-22202022220000-22-22-2-2000000002020-20-200000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000
χ24222222-22-22202022220000-22-22-2-2000000002020-20-200000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000
χ25222222-22-22-20-2022220000-22-22-2-200000000-20-2020200000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000
χ26222222-22-22-20-2022220000-22-22-2-200000000-20-2020200000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000
χ27222222-2-2-2-2000022220000-2-2-2-22200000000000000002-2-222-2-222-2-220000000000000000
χ28222222-2-2-2-2000022220000-2-2-2-22200000000000000002-2-22-222-2-222-20000000000000000
χ29222222-2-2-2-2000022220000-2-2-2-2220000000000000000-222-2000000002-2-222-2-2200000000
χ30222222-2-2-2-2000022220000-2-2-2-2220000000000000000-222-200000000-222-2-222-200000000
χ312-222-2-222-2-22i−2i−2i2i22-2-2000022-2-2-22000000002i−2i−2i2i2i−2i−2i2i-22-22000000000000000000000000
χ322-222-2-222-2-2−2i2i2i−2i22-2-2000022-2-2-2200000000−2i2i2i−2i−2i2i2i−2i-22-22000000000000000000000000
χ332-222-2-22-2-2202i0−2i22-2-200002-2-222-20000000002i0−2i0−2i02i000022−2−2−2−222−i2−i2i2i2i2i2−i2−i200000000
χ342-222-2-22-2-2202i0−2i22-2-200002-2-222-20000000002i0−2i0−2i02i0000−2−22222−2−2i2i2−i2−i2−i2−i2i2i200000000
χ352-222-2-22-2-220−2i02i22-2-200002-2-222-2000000000−2i02i02i0−2i000022−2−2−2−222i2i2−i2−i2−i2−i2i2i200000000
χ362-222-2-22-2-220−2i02i22-2-200002-2-222-2000000000−2i02i02i0−2i0000−2−22222−2−2−i2−i2i2i2i2i2−i2−i200000000
χ372-222-2-2-222-22i0−2i022-2-20000-222-22-2000000002i0−2i0−2i02i000002−22−2−22−22−i2i2−i2i2i2−i2i2−i200000000
χ382-222-2-2-222-22i0−2i022-2-20000-222-22-2000000002i0−2i0−2i02i00000−22−222−22−2i2−i2i2−i2−i2i2−i2i200000000
χ392-222-2-2-222-2−2i02i022-2-20000-222-22-200000000−2i02i02i0−2i000002−22−2−22−22i2−i2i2−i2−i2i2−i2i200000000
χ402-222-2-2-222-2−2i02i022-2-20000-222-22-200000000−2i02i02i0−2i00000−22−222−22−2−i2i2−i2i2i2−i2i2−i200000000
χ412-222-2-2-2-222000022-2-20000-2-222-22000000000000000022-2-22i−2i−2i2i−2i2i2i−2i0000000000000000
χ422-222-2-2-2-222000022-2-20000-2-222-22000000000000000022-2-2−2i2i2i−2i2i−2i−2i2i0000000000000000
χ432-222-2-2-2-222000022-2-20000-2-222-220000000000000000-2-222000000002-2-22-222-200000000
χ442-222-2-2-2-222000022-2-20000-2-222-220000000000000000-2-22200000000-222-22-2-2200000000
χ45888-18-108088080-1-1-1-122220-10-1002-12-12-12-1-10-10000000000000000000000000-1-1-1-10000
χ46888-18-108088080-1-1-1-1-2-2-2-20-10-100-21-21-21-21-10-1000000000000000000000000011110000
χ47888-18-10808-80-80-1-1-1-122-2-20-10-1002-12-1-21-211010000000000000000000000000-1-1110000
χ48888-18-10808-80-80-1-1-1-1-2-2220-10-100-21-212-12-1101000000000000000000000000011-1-10000
χ4988-18-1880800808-1-1-1-12222-10-1000-12-12-12-120-10-1000000000000000000000000-1-1-1-10000
χ5088-18-1880800808-1-1-1-1-2-2-2-2-10-10001-21-21-21-20-10-100000000000000000000000011110000
χ5188-18-1880800-80-8-1-1-1-122-2-2-10-1000-12-121-21-20101000000000000000000000000-1-1110000
χ5288-18-1880800-80-8-1-1-1-1-2-222-10-10001-21-2-12-12010100000000000000000000000011-1-10000
χ538-88-1-81080-88i0−8i0-1-1112-22i−2i0-101002-1-212i−i−2ii−i0i0000000000000000000000000-11−ii0000
χ548-88-1-81080-88i0−8i0-1-111-22−2i2i0-10100-212-1−2ii2i−i−i0i00000000000000000000000001-1i−i0000
χ558-88-1-81080-8−8i08i0-1-1112-2−2i2i0-101002-1-21−2ii2i−ii0−i0000000000000000000000000-11i−i0000
χ568-88-1-81080-8−8i08i0-1-111-222i−2i0-10100-212-12i−i−2iii0−i00000000000000000000000001-1−ii0000
χ578-8-181-880-8008i0−8i-1-1112-22i−2i-101000-121-2−i2ii−2i0−i0i000000000000000000000000-11−ii0000
χ588-8-181-880-8008i0−8i-1-111-22−2i2i-1010001-2-12i−2i−i2i0−i0i0000000000000000000000001-1i−i0000
χ598-8-181-880-800−8i08i-1-1112-2−2i2i-101000-121-2i−2i−i2i0i0−i000000000000000000000000-11i−i0000
χ608-8-181-880-800−8i08i-1-111-222i−2i-1010001-2-12−i2ii−2i0i0−i0000000000000000000000001-1−ii0000
χ61161616-216-20-160-160000-2-2-2-2000002020000000000000000000000000000000000000000000000
χ621616-216-216-160-1600000-2-2-2-2000020200000000000000000000000000000000000000000000000
χ6316-1616-2-1620-160160000-2-2220000020-20000000000000000000000000000000000000000000000
χ6416-16-2162-16-1601600000-2-222000020-200000000000000000000000000000000000000000000000
χ653232-4-4-4-4000000005-4-4500440000000000-2-2-2-2000000000000000000000000000000110000
χ663232-4-4-4-4000000005-4-4500-4-400000000002222000000000000000000000000000000-1-10000
χ673232-4-4-4-400000000-455-44400000000-2-2-2-20000000000000000000000000000000011000000
χ683232-4-4-4-400000000-455-4-4-400000000222200000000000000000000000000000000-1-1000000
χ6932-32-4-444000000005-44-5004i−4i0000000000−2i−2i2i2i000000000000000000000000000000i−i0000
χ7032-32-4-444000000005-44-500−4i4i00000000002i2i−2i−2i000000000000000000000000000000−ii0000
χ7132-32-4-44400000000-45-544-400000000-2-222000000000000000000000000000000001-1000000
χ7232-32-4-44400000000-45-54-440000000022-2-200000000000000000000000000000000-11000000

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