Finite Group Databasebeta

← Group #72230437

Character table — Group #72230437

Order 2880.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1122222444444445588888888810101010101212121212121616161618182020202020202424242424242424242424244040404040404040406060606060606060606072729090120120120120180180
order123346635610121220202212151530306060606046666882424242415306060244466121240404040120120120120120120120120121212121212121212444488242424241020241212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ311111111111111111111111111111111-111-1-11111-1-111111111-1-11111-1-1-1-111111111111-1-11-111-1-1-1-1-1-111-1-1-1-1
χ411111111111111111111111111111111-111-1-11111-1-1-1-1111111-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111-11-1-1111111-1-1111111-1-111-1-1-1-11111111111111-1-111-11-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111-11-1-1111111-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-11-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ9111111111111111-1-1111111111-1-1-1-1-1111111111111i−i-1-1-1-1111111111111-1i−ii−iii−i−ii−ii−i-1-1-1-1-1-111-1-1i−ii−ii−i
χ10111111111111111-1-1111111111-1-1-1-1-1111111111111−ii-1-1-1-1111111111111-1−ii−ii−i−iii−ii−ii-1-1-1-1-1-111-1-1−ii−ii−ii
χ11111111111111111-1-1111111111-1-1-1-1-11-111-1-11111-1-1i−i-1-1-1-111-1-11111-1-1-1-1-1i−ii−iii−i−ii−i−ii-11-1-111-1-111i−i−ii−ii
χ12111111111111111-1-1111111111-1-1-1-1-11-111-1-11111-1-1−ii-1-1-1-111-1-11111-1-1-1-1-1−ii−ii−i−iii−iii−i-11-1-111-1-111−iii−ii−i
χ13111111111111111-1-1111111111-1-1-1-1-1-11-1-1111111-1-1i−i-1-1-1-1-1-111-1-1-1-11111-1i−ii−iii−i−i−iii−i1-111-1-1-1-111−iii−i−ii
χ14111111111111111-1-1111111111-1-1-1-1-1-11-1-1111111-1-1−ii-1-1-1-1-1-111-1-1-1-11111-1−ii−ii−i−iiii−i−ii1-111-1-1-1-111i−i−iii−i
χ15111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1111111i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−ii−iii−i−i−ii−ii11111111-1-1−ii−iii−i
χ16111111111111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1111111−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii−ii−i−iiii−ii−i11111111-1-1i−ii−i−ii
χ172222-2222222-2-2-2-222-22222-2-2-2-2-2222200000022-2-22-20022-2-2000000000000-20000000000000000002-22-2000000
χ182222-2222222-2-2-2-222-22222-2-2-2-2-2222200000022-2-2-220022-2-2000000000000-2000000000000000000-22-22000000
χ192222-2222222-2-2-2-2-2-2-22222-2-2-2-22-2-2-2-200000022-2-22-200-2-22200000000000020000000000000000002-2-22000000
χ202222-2222222-2-2-2-2-2-2-22222-2-2-2-22-2-2-2-200000022-2-2-2200-2-2220000000000002000000000000000000-222-2000000
χ21222-122-1-12-122-12222-12-12-122-1-122-1-1220-1-100-1-1-1-10022-1-12-12200-1-1-1-10000-1-1-122-1-1-1-1220020-1-1000000-1-10000
χ22222-122-1-12-122-12222-12-12-122-1-122-1-1220-1-100-1-1-1-100-2-2-1-12-12200-1-1-1-10000-111-2-21111-2-20020-1-1000000110000
χ23222-122-1-12-122-12222-12-12-122-1-122-1-12-201100-1-1-1-10022-1-12-1-2-20011110000-1-1-122-1-1-1-1-2-200-2011000000110000
χ24222-122-1-12-122-12222-12-12-122-1-122-1-12-201100-1-1-1-100-2-2-1-12-1-2-20011110000-111-2-211112200-2011000000-1-10000
χ25222-122-1-12-122-122-2-2-12-12-122-1-1-2-211-220-1-100-1-1-1-1002i−2i11-212200-1-1-1-100001−ii2i−2i−i−iii2i−2i00-2011000000−ii0000
χ26222-122-1-12-122-122-2-2-12-12-122-1-1-2-211-220-1-100-1-1-1-100−2i2i11-212200-1-1-1-100001i−i−2i2iii−i−i−2i2i00-2011000000i−i0000
χ27222-122-1-12-122-122-2-2-12-12-122-1-1-2-211-2-201100-1-1-1-1002i−2i11-21-2-200111100001−ii2i−2i−i−iii−2i2i0020-1-1000000i−i0000
χ28222-122-1-12-122-122-2-2-12-12-122-1-1-2-211-2-201100-1-1-1-100−2i2i11-21-2-200111100001i−i−2i2iii−i−i2i−2i0020-1-1000000−ii0000
χ2922-122-12-12-12-122222-1-12-12-1-1222-122-10200-1-1-1-1-1-10022-1-1-1200220000-1-1-1-1-122-1-1-1-1-1-100220200-1-1000000-1-100
χ3022-122-12-12-12-122222-1-12-12-1-1222-122-10200-1-1-1-1-1-100-2-2-1-1-1200220000-1-1-1-1-1-2-211111100-2-20200-1-10000001100
χ3122-122-12-12-12-122222-1-12-12-1-1222-122-10-20011-1-1-1-10022-1-1-1200-2-200001111-122-1-1-1-1-1-100-2-20-200110000001100
χ3222-122-12-12-12-122222-1-12-12-1-1222-122-10-20011-1-1-1-100-2-2-1-1-1200-2-200001111-1-2-211111100220-20011000000-1-100
χ3322-122-12-12-12-1222-2-2-1-12-12-1-122-21-2-210200-1-1-1-1-1-1002i−2i111-200220000-1-1-1-112i−2i−ii−i−iii002i−2i0-20011000000−ii00
χ3422-122-12-12-12-1222-2-2-1-12-12-1-122-21-2-210200-1-1-1-1-1-100−2i2i111-200220000-1-1-1-11−2i2ii−iii−i−i00−2i2i0-20011000000i−i00
χ3522-122-12-12-12-1222-2-2-1-12-12-1-122-21-2-210-20011-1-1-1-1002i−2i111-200-2-20000111112i−2i−ii−i−iii00−2i2i0200-1-1000000i−i00
χ3622-122-12-12-12-1222-2-2-1-12-12-1-122-21-2-210-20011-1-1-1-100−2i2i111-200-2-2000011111−2i2ii−iii−i−i002i−2i0200-1-1000000−ii00
χ3744444444-14-144-1-1004-1-1-1-1-1-1-1-100000444444-1-1-1-144000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000-1-100000000
χ3844444444-14-144-1-1004-1-1-1-1-1-1-1-1000004-444-4-4-1-1-1-1-4-4000000-1-111-1-1-1-1111100000000000000000001100000000
χ3944444444-14-144-1-1004-1-1-1-1-1-1-1-100000-44-4-444-1-1-1-1-4-400000011-1-11111-1-1-1-100000000000000000001100000000
χ4044444444-14-144-1-1004-1-1-1-1-1-1-1-100000-4-4-4-4-4-4-1-1-1-1440000001111111111110000000000000000000-1-100000000
χ414444-4444-14-1-4-41100-4-1-1-1-1111100000000000-1-1114-4000000−i5i5−i5i5−i5−i5i5i5−i5−i5i5i50000000000000000000-1100000000
χ424444-4444-14-1-4-41100-4-1-1-1-1111100000000000-1-1114-4000000i5−i5i5−i5i5i5−i5−i5i5i5−i5−i50000000000000000000-1100000000
χ434444-4444-14-1-4-41100-4-1-1-1-1111100000000000-1-111-44000000−i5i5i5−i5−i5−i5i5i5i5i5−i5−i500000000000000000001-100000000
χ444444-4444-14-1-4-41100-4-1-1-1-1111100000000000-1-111-44000000i5−i5−i5i5i5i5−i5−i5−i5−i5i5i500000000000000000001-100000000
χ45444-2-44-2-24-24-42-4-44424-24-2-4-422-44-2-24000000-2-2220000-2-2-4200000000000020000000000000000000000000000
χ46444-2-44-2-24-24-42-4-4-4-424-24-2-4-4224-422-4000000-2-2220000224-2000000000000-20000000000000000000000000000
χ4744-24-4-24-24-242-4-4-4442-24-2422-4-4-4-244-2000000-2-2220000-2-22-400000000000020000000000000000000000000000
χ4844-24-4-24-24-242-4-4-4-4-42-24-2422-4-442-4-42000000-2-222000022-24000000000000-20000000000000000000000000000
χ4944-2-24-2-21414-2-244441-2-2-2-2-2-2-2-24-2-2-2-20000001111004411-2-20000000000001-2-2-2-2111100000000000000000000
χ5044-2-24-2-21414-2-244441-2-2-2-2-2-2-2-24-2-2-2-2000000111100-4-411-2-200000000000012222-1-1-1-100000000000000000000
χ5144-2-24-2-21414-2-244-4-41-2-2-2-2-2-2-2-2-422220000001111004i−4i-1-122000000000000-1−2i2i−2i2iii−i−i00000000000000000000
χ5244-2-24-2-21414-2-244-4-41-2-2-2-2-2-2-2-2-42222000000111100−4i4i-1-122000000000000-12i−2i2i−2i−i−iii00000000000000000000
χ5344-2-2-4-2-2141422-4-444-1-2-2-2-22222-4-2-2-2-200000011-1-100001122000000000000-100003-33-300000000000000000000
χ5444-2-2-4-2-2141422-4-444-1-2-2-2-22222-4-2-2-2-200000011-1-100001122000000000000-10000-33-3300000000000000000000
χ5544-2-2-4-2-2141422-4-4-4-4-1-2-2-2-222224222200000011-1-10000-1-1-2-2000000000000100003i−3i−3i3i00000000000000000000
χ5644-2-2-4-2-2141422-4-4-4-4-1-2-2-2-222224222200000011-1-10000-1-1-2-200000000000010000−3i3i3i−3i00000000000000000000
χ574-4440-4-444-4-400004-4044-4-4000004-44-40000004-40000004-40000000000000000000000000000000000000000000
χ584-4440-4-444-4-40000-44044-4-400000-44-440000004-4000000-440000000000000000000000000000000000000000000
χ594-44-20-42-242-400004-404-2-420000042-2-4006−600-22000000-220000006−66−600000000000000000006−6000000000000
χ604-44-20-42-242-400004-404-2-420000042-2-400−6600-22000000-22000000−66−660000000000000000000−66000000000000
χ614-44-20-42-242-40000-4404-2-4200000-4-224006−600-220000002-20000006−66−60000000000000000000−66000000000000
χ624-44-20-42-242-40000-4404-2-4200000-4-22400−6600-220000002-2000000−66−6600000000000000000006−6000000000000
χ634-4-2402-4-242-400004-40-242-400000-2-4420000−i6i6-22000000-220000000000−i6i6−i6i600000000000000000−i6i60000000000
χ644-4-2402-4-242-400004-40-242-400000-2-4420000i6−i6-22000000-220000000000i6−i6i6−i600000000000000000i6−i60000000000
χ654-4-2402-4-242-40000-440-242-40000024-4-20000−i6i6-220000002-20000000000−i6i6−i6i600000000000000000i6−i60000000000
χ664-4-2402-4-242-40000-440-242-40000024-4-20000i6−i6-220000002-20000000000i6−i6i6−i600000000000000000−i6i60000000000
χ67888-488-4-4-2-4-28-4-2-200-4-21-21-2-2110000080-4-400111100000000-2-2001111000000000000000000000000000000000
χ68888-488-4-4-2-4-28-4-2-200-4-21-21-2-21100000-8044001111000000002200-1-1-1-1000000000000000000000000000000000
χ69888-4-88-4-4-2-4-2-8422004-21-2122-1-10000000000011-1-100000000−2i52i500i5i5−i5−i5000000000000000000000000000000000
χ70888-4-88-4-4-2-4-2-8422004-21-2122-1-10000000000011-1-1000000002i5−2i500−i5−i5i5i5000000000000000000000000000000000
χ7188-488-48-4-2-4-2-48-2-200-41-21-211-2-2000000800-4-411110000000000-2-20000111100000000000000000000000000000
χ7288-488-48-4-2-4-2-48-2-200-41-21-211-2-2000000-8004411110000000000220000-1-1-1-100000000000000000000000000000
χ7388-48-8-48-4-2-4-24-8220041-21-2-1-1220000000000011-1-10000000000−2i52i50000i5i5−i5−i500000000000000000000000000000
χ7488-48-8-48-4-2-4-24-8220041-21-2-1-1220000000000011-1-100000000002i5−2i50000−i5−i5i5i500000000000000000000000000000
χ758-8880-8-88-2-8200−2i52i5000-2-222−2i52i5−2i52i500000000000-22−2i52i50000000000000000000000000000000000000000000000000
χ768-8880-8-88-2-82002i5−2i5000-2-2222i5−2i52i5−2i500000000000-222i5−2i50000000000000000000000000000000000000000000000000
χ778-88-40-84-4-24200−2i52i5000-212-1−2i52i5i5−i5000000026−26001-1i5−i5000000000000−ζ13−ζ31−ζ37+ζ53+ζ71+ζ77−ζ79+ζ119ζ13+ζ31+ζ37−ζ53−ζ71−ζ77+ζ79−ζ119−ζ7+ζ23+ζ29+ζ47−ζ61+ζ101−ζ103−ζ109ζ7−ζ23−ζ29−ζ47+ζ61−ζ101+ζ103+ζ109000000000000000000000000000000000
χ788-88-40-84-4-24200−2i52i5000-212-1−2i52i5i5−i50000000−2626001-1i5−i5000000000000ζ13+ζ31+ζ37−ζ53−ζ71−ζ77+ζ79−ζ119−ζ13−ζ31−ζ37+ζ53+ζ71+ζ77−ζ79+ζ119ζ7−ζ23−ζ29−ζ47+ζ61−ζ101+ζ103+ζ109−ζ7+ζ23+ζ29+ζ47−ζ61+ζ101−ζ103−ζ109000000000000000000000000000000000
χ798-88-40-84-4-242002i5−2i5000-212-12i5−2i5−i5i5000000026−26001-1−i5i5000000000000−ζ7+ζ23+ζ29+ζ47−ζ61+ζ101−ζ103−ζ109ζ7−ζ23−ζ29−ζ47+ζ61−ζ101+ζ103+ζ109−ζ13−ζ31−ζ37+ζ53+ζ71+ζ77−ζ79+ζ119ζ13+ζ31+ζ37−ζ53−ζ71−ζ77+ζ79−ζ119000000000000000000000000000000000
χ808-88-40-84-4-242002i5−2i5000-212-12i5−2i5−i5i50000000−2626001-1−i5i5000000000000ζ7−ζ23−ζ29−ζ47+ζ61−ζ101+ζ103+ζ109−ζ7+ζ23+ζ29+ζ47−ζ61+ζ101−ζ103−ζ109ζ13+ζ31+ζ37−ζ53−ζ71−ζ77+ζ79−ζ119−ζ13−ζ31−ζ37+ζ53+ζ71+ζ77−ζ79+ζ119000000000000000000000000000000000
χ818-8-4804-8-4-24200−2i52i50001-2-12i5−i5−2i52i5000000000−2i62i61-1i5−i50000000000000000−ζ7+ζ23−ζ29+ζ47+ζ61−ζ101−ζ103+ζ109ζ7−ζ23+ζ29−ζ47−ζ61+ζ101+ζ103−ζ109ζ13−ζ31+ζ37−ζ53+ζ71−ζ77−ζ79+ζ119−ζ13+ζ31−ζ37+ζ53−ζ71+ζ77+ζ79−ζ11900000000000000000000000000000
χ828-8-4804-8-4-24200−2i52i50001-2-12i5−i5−2i52i50000000002i6−2i61-1i5−i50000000000000000ζ7−ζ23+ζ29−ζ47−ζ61+ζ101+ζ103−ζ109−ζ7+ζ23−ζ29+ζ47+ζ61−ζ101−ζ103+ζ109−ζ13+ζ31−ζ37+ζ53−ζ71+ζ77+ζ79−ζ119ζ13−ζ31+ζ37−ζ53+ζ71−ζ77−ζ79+ζ11900000000000000000000000000000
χ838-8-4804-8-4-242002i5−2i50001-2-12−i5i52i5−2i5000000000−2i62i61-1−i5i50000000000000000ζ13−ζ31+ζ37−ζ53+ζ71−ζ77−ζ79+ζ119−ζ13+ζ31−ζ37+ζ53−ζ71+ζ77+ζ79−ζ119−ζ7+ζ23−ζ29+ζ47+ζ61−ζ101−ζ103+ζ109ζ7−ζ23+ζ29−ζ47−ζ61+ζ101+ζ103−ζ10900000000000000000000000000000
χ848-8-4804-8-4-242002i5−2i50001-2-12−i5i52i5−2i50000000002i6−2i61-1−i5i50000000000000000−ζ13+ζ31−ζ37+ζ53−ζ71+ζ77+ζ79−ζ119ζ13−ζ31+ζ37−ζ53+ζ71−ζ77−ζ79+ζ119ζ7−ζ23+ζ29−ζ47−ζ61+ζ101+ζ103−ζ109−ζ7+ζ23−ζ29+ζ47+ζ61−ζ101−ζ103+ζ10900000000000000000000000000000
χ858-8-4-404428-2-800008-80-4-44400000-44-440000002-20000002-20000000000000000000000000000000000000000000
χ868-8-4-404428-2-80000-880-4-444000004-44-40000002-2000000-220000000000000000000000000000000000000000000
χ871616-8-816-8-84-44-4-8-8-4-40042222222200000000000-1-1-1-10000000000000000000000000000000000000000000000000
χ881616-8-8-16-8-84-44-4884400-42222-2-2-2-200000000000-1-1110000000000000000000000000000000000000000000000000
χ8916-16-8-80884-4-4400−4i54i500022-2-22i5−2i52i5−2i500000000000-11−i5i50000000000000000000000000000000000000000000000000
χ9016-16-8-80884-4-44004i5−4i500022-2-2−2i52i5−2i52i500000000000-11i5−i50000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 120 (ζ120 = 1); i = ζ30.