Finite Group Databasebeta

← Group #14514373

Character table — Group #14514373

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70
size1122233445566688888101010121215151616161616161624242430303030303030303030303232323232324040606060606060606060606060808080
order1244422510444443620202022210104412121215153030202020222888888886060606060601212888888888888666
χ11111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111
χ3111111111-1-111111111-1-1-111-1-11111111111-1-1-1ii−i−iii−i−i111111-1-1iii−i−i−iiii−i−i−i-1-1-1
χ4111111111-1-111111111-1-1-111-1-11111111111-1-1-1−i−iii−i−iii111111-1-1−i−i−iiii−i−i−iiii-1-1-1
χ5111-1-11111111-1-1111-1-11-1-111111-1-111111-1-11-1-11111111111-1-1-1-1111-1-11-1-11-1-11-1-11-1-1
χ6111-1-11111111-1-1111-1-11-1-111111-1-111111-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-111-111-111-111-1111-1-1
χ7111-1-11111-1-11-1-1111-1-1-11111-1-11-1-111111-1-1-111ii−i−iii−i−i11-1-1-1-1-1-1i−i−i−iiii−i−i−iii-111
χ8111-1-11111-1-11-1-1111-1-1-11111-1-11-1-111111-1-1-111−i−iii−i−iii11-1-1-1-1-1-1−iiii−i−i−iiii−i−i-111
χ911-11-1111111-11-111-11-1-11-11111-11-11111-11-1-11-111111111-1-111-1-111-11-1-11-1-11-1-11-1-11-1
χ1011-11-1111111-11-111-11-1-11-11111-11-11111-11-1-11-1-1-1-1-1-1-1-1-1-1-111-1-1111-111-111-111-11-11-1
χ1111-11-11111-1-1-11-111-11-11-1111-1-1-11-11111-11-11-11ii−i−iii−i−i-1-111-1-1-1-1−ii−ii−ii−ii−ii−ii1-11
χ1211-11-11111-1-1-11-111-11-11-1111-1-1-11-11111-11-11-11−i−iii−i−iii-1-111-1-1-1-1i−ii−ii−ii−ii−ii−i1-11
χ1311-1-11111111-1-1111-1-11-1-111111-1-111111-1-11-1-1111111111-1-1-1-11111-1-11-1-11-1-11-1-11-1-11
χ1411-1-11111111-1-1111-1-11-1-111111-1-111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-111-111-111-1-1-11
χ1511-1-111111-1-1-1-1111-1-1111-111-1-1-1-111111-1-1111-1ii−i−iii−i−i-1-1-1-111-1-1−i−iiii−i−i−iiii−i11-1
χ1611-1-111111-1-1-1-1111-1-1111-111-1-1-1-111111-1-1111-1−i−iii−i−iii-1-1-1-111-1-1ii−i−i−iiii−i−i−ii11-1
χ1722222222222222-1-12222222222-1-1-1-1-1-1-122222200000000-1-1-1-1-1-1-1-1000000000000-1-1-1
χ18222222222-2-2222-1-1222-2-2-222-2-2-1-1-1-1-1-1-1222-2-2-200000000-1-1-1-1-1-111000000000000111
χ19222-2-22222222-2-2-1-12-2-22-2-22222-111-1-1-1-12-2-22-2-200000000-1-11111-1-1000000000000-111
χ20222-2-22222-2-22-2-2-1-12-2-2-22222-2-2-111-1-1-1-12-2-2-22200000000-1-11111110000000000001-1-1
χ2122-22-2222222-22-2-1-1-22-2-22-222221-11-1-1-1-1-22-2-22-20000000011-1-111-1-10000000000001-11
χ2222-22-22222-2-2-22-2-1-1-22-22-2222-2-21-11-1-1-1-1-22-22-220000000011-1-11111000000000000-11-1
χ2322-2-22222222-2-22-1-1-2-22-2-22222211-1-1-1-1-1-2-22-2-22000000001111-1-1-1-100000000000011-1
χ2422-2-222222-2-2-2-22-1-1-2-2222-222-2-211-1-1-1-1-1-2-2222-2000000001111-1-111000000000000-1-11
χ252-20002-22-22i−2i0002-20000002-22i−2i00022-2-20000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1090000002i−2i000000000000000
χ262-20002-22-22i−2i0002-20000002-22i−2i00022-2-2000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1090000002i−2i000000000000000
χ272-20002-22-2−2i2i0002-20000002-2−2i2i00022-2-2000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119000000−2i2i000000000000000
χ282-20002-22-2−2i2i0002-20000002-2−2i2i00022-2-20000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119000000−2i2i000000000000000
χ2933333-1-13333-1-1-100333333-1-1-1-10000000-1-1-1-1-1-11111-1-1-1-100000000111111-1-1-1-1-1-1000
χ3033333-1-13333-1-1-100333333-1-1-1-10000000-1-1-1-1-1-1-1-1-1-1111100000000-1-1-1-1-1-1111111000
χ3133333-1-133-3-3-1-1-100333-3-3-3-1-1110000000-1-1-1111ii−i−i−i−iii00000000iii−i−i−i−i−i−iiii000
χ3233333-1-133-3-3-1-1-100333-3-3-3-1-1110000000-1-1-1111−i−iiiii−i−i00000000−i−i−iiiiiii−i−i−i000
χ33333-3-3-1-13333-111003-3-33-3-3-1-1-1-10000000-111-1111111-1-1-1-1000000001-1-11-1-1-111-111000
χ34333-3-3-1-13333-111003-3-33-3-3-1-1-1-10000000-111-111-1-1-1-1111100000000-111-1111-1-11-1-1000
χ35333-3-3-1-133-3-3-111003-3-3-333-1-1110000000-1111-1-1ii−i−i−i−iii00000000i−i−i−iii−iiii−i−i000
χ36333-3-3-1-133-3-3-111003-3-3-333-1-1110000000-1111-1-1−i−iiiii−i−i00000000−iiii−i−ii−i−i−iii000
χ3733-33-3-1-133331-1100-33-3-33-3-1-1-1-100000001-111-111111-1-1-1-100000000-11-1-11-11-111-11000
χ3833-33-3-1-133331-1100-33-3-33-3-1-1-1-100000001-111-11-1-1-1-11111000000001-111-11-11-1-11-1000
χ3933-33-3-1-133-3-31-1100-33-33-33-1-11100000001-11-11-1ii−i−i−i−iii00000000−ii−ii−iii−ii−ii−i000
χ4033-33-3-1-133-3-31-1100-33-33-33-1-11100000001-11-11-1−i−iiiii−i−i00000000i−ii−ii−i−ii−ii−ii000
χ4133-3-33-1-1333311-100-3-33-3-33-1-1-1-1000000011-111-11111-1-1-1-100000000-1-11-1-1111-111-1000
χ4233-3-33-1-1333311-100-3-33-3-33-1-1-1-1000000011-111-1-1-1-1-111110000000011-111-1-1-11-1-11000
χ4333-3-33-1-133-3-311-100-3-3333-3-1-111000000011-1-1-11ii−i−i−i−iii00000000−i−iiii−iii−i−i−ii000
χ4433-3-33-1-133-3-311-100-3-3333-3-1-111000000011-1-1-11−i−iiiii−i−i00000000ii−i−i−ii−i−iiii−i000
χ454444444-1-10044444-1-1-1000-1-100444-1-1-1-1-1-1-100000000000-1-1-1-1-1-100000000000000000
χ464444444-1-100444-2-2-1-1-1000-1-100-2-2-21−i1521+i1521−i1521+i152-1-1-1000000000001−i1521+i1521−i1521+i1521−i1521+i15200000000000000000
χ474444444-1-100444-2-2-1-1-1000-1-100-2-2-21+i1521−i1521+i1521−i152-1-1-1000000000001+i1521−i1521+i1521−i1521+i1521−i15200000000000000000
χ48444-4-444-1-1004-4-444-111000-1-1004-4-4-1-1-1-1-11100000000000-1-1111100000000000000000
χ49444-4-444-1-1004-4-4-2-2-111000-1-100-2221−i1521+i1521−i1521+i152-111000000000001−i1521+i152−1+i152−1−i152−1+i152−1−i15200000000000000000
χ50444-4-444-1-1004-4-4-2-2-111000-1-100-2221+i1521−i1521+i1521−i152-111000000000001+i1521−i152−1−i152−1+i152−1−i152−1+i15200000000000000000
χ5144-44-444-1-100-44-4441-11000-1-100-44-4-1-1-1-11-110000000000011-1-11100000000000000000
χ5244-44-444-1-100-44-4-2-21-11000-1-1002-221−i1521+i1521−i1521+i1521-1100000000000−1+i152−1−i1521−i1521+i152−1+i152−1−i15200000000000000000
χ5344-44-444-1-100-44-4-2-21-11000-1-1002-221+i1521−i1521+i1521−i1521-1100000000000−1−i152−1+i1521+i1521−i152−1−i152−1+i15200000000000000000
χ5444-4-4444-1-100-4-444411-1000-1-100-4-44-1-1-1-111-1000000000001111-1-100000000000000000
χ5544-4-4444-1-100-4-44-2-211-1000-1-10022-21−i1521+i1521−i1521+i15211-100000000000−1+i152−1−i152−1+i152−1−i1521−i1521+i15200000000000000000
χ5644-4-4444-1-100-4-44-2-211-1000-1-10022-21+i1521−i1521+i1521−i15211-100000000000−1−i152−1+i152−1−i152−1+i1521+i1521−i15200000000000000000
χ574-40004-44-44i−4i000-220000004-44i−4i000-2-22200000000000000000000−2i2i000000000000000
χ584-40004-44-4−4i4i000-220000004-4−4i4i000-2-222000000000000000000002i−2i000000000000000
χ596-6000-226-66i−6i00000000000-22−2i2i00000000000002ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ10900000000000000000000000
χ606-6000-226-66i−6i00000000000-22−2i2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ10900000000000000000000000
χ616-6000-226-6−6i6i00000000000-222i−2i0000000000000−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ11900000000000000000000000
χ626-6000-226-6−6i6i00000000000-222i−2i00000000000002ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ109−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ109−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ1192ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ13−2ζ29−2ζ37−2ζ53−2ζ61−2ζ77−2ζ101−2ζ1092ζ13+2ζ29+2ζ37+2ζ53+2ζ61+2ζ77+2ζ101+2ζ1092ζ7+2ζ23+2ζ31+2ζ47+2ζ71+2ζ79+2ζ103+2ζ119−2ζ7−2ζ23−2ζ31−2ζ47−2ζ71−2ζ79−2ζ103−2ζ11900000000000000000000000
χ638-80008-8-22000008-8000000-2200000-2-2220000000000000000000000000000000000000
χ648-80008-8-2200000-44000000-22000001−i151+i15−1+i15−1−i150000000000000000000000000000000000000
χ658-80008-8-2200000-44000000-22000001+i151−i15−1−i15−1+i150000000000000000000000000000000000000
χ661212121212-4-4-3-300-4-4-400-3-3-3000110000000001110000000000000000000000000000000000
χ67121212-12-12-4-4-3-300-44400-333000110000000001-1-10000000000000000000000000000000000
χ681212-1212-12-4-4-3-3004-44003-3300011000000000-11-10000000000000000000000000000000000
χ691212-12-1212-4-4-3-30044-40033-300011000000000-1-110000000000000000000000000000000000
χ7024-24000-88-6600000000000002-20000000000000000000000000000000000000000000000

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