Finite Group Databasebeta

← Group #72258816

Character table — Group #72258816

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222444444444444444444444444448888888888881616161616161616161616161616161616161616161624242424242424242424242432323232323248484848484848484848
order12222234444666444466888888881212121224242424242424244444121212122424242488121212121616161624242424484848484848484822448888888822666644448816161616
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ81111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ911-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1ii−i−i11-1-111-1-1i−iii−i−iii−i−iii−i−iiiii−i−i−i−i1-11-1iiii−i−i−i−i1-111-1-1ii−i−i1-111-1-1
χ1011-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1ii−i−i11-1-111-1-1i−iii−i−iii−i−iii−i−iiiii−i−i−i−i-11-11−i−i−i−iiiii1-111-1-1−i−iii-11-1-111
χ1111-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1ii−i−i11-1-111-1-1i−iii−i−i−i−iiiii−i−i−i−i−i−iiiii1-11-1−i−i−i−iiiii-11-1-111ii−i−i1-1-1-111
χ1211-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1ii−i−i11-1-111-1-1i−iii−i−i−i−iiiii−i−i−i−i−i−iiiii-11-11iiii−i−i−i−i-11-1-111−i−iii-1111-1-1
χ1311-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1−i−iii11-1-111-1-1−ii−i−iiiii−i−i−i−iiiiiii−i−i−i−i1-11-1iiii−i−i−i−i-11-1-111−i−iii1-1-1-111
χ1411-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1−i−iii11-1-111-1-1−ii−i−iiiii−i−i−i−iiiiiii−i−i−i−i-11-11−i−i−i−iiiii-11-1-111ii−i−i-1111-1-1
χ1511-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1−i−iii11-1-111-1-1−ii−i−iii−i−iii−i−iii−i−i−i−iiiii1-11-1−i−i−i−iiiii1-111-1-1−i−iii1-111-1-1
χ1611-1-1-111-11-111-1-111-1-1-111-1-111-1-11-111-11111-1-1-1-1−i−iii11-1-111-1-1−ii−i−iii−i−iii−i−iii−i−i−i−iiiii-11-11iiii−i−i−i−i1-111-1-1ii−i−i-11-1-111
χ1722222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-200000000000000000000000000000000000000002-22-2000000
χ1822222222222222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000000000000000000000000000-22-22000000
χ1922222222222222-2-2-2-222222-2-2-2-22222222-2-222-2-20000-2-2-2-22-22-200000000000000000000002222000000000000000000-2-20000
χ2022222222222222-2-2-2-222222-2-2-2-22222222-2-222-2-20000-2-2-2-22-22-20000000000000000000000-2-2-2-2000000000000000000220000
χ2122222222222222-2-2-2-222-2-2-22222-22222-2-222-2-2222222-2-2-2-2-22-22-2-222220000-2-2-2-2000000000000000000000000000000000000
χ2222222222222222-2-2-2-222-2-2-22222-22222-2-222-2-222-2-2-2-2-2-2-2-2-22-2222-2-2-2-200002222000000000000000000000000000000000000
χ23222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-10000000000
χ24222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-2-2-2-2-1-1-1-111111111000000000000-2-211110000000000
χ25222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-2111122221111-1-1-1-1-1-1-1-1000000000000-2-211110000000000
χ26222222-12222-1-1-12222-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-2-21111-2-2-2-211111111111100000000000022-1-1-1-10000000000
χ27222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-111-1-111-1-1222211111-11-1-2-2-1-1-1-100001111−i3−i3i3i3−i3−i3i3i300000000000000−i3i3−i3i30000000000
χ28222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-111-1-111-1-1222211111-11-1-2-2-1-1-1-100001111i3i3−i3−i3i3i3−i3−i300000000000000i3−i3i3−i30000000000
χ29222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-111-1-111-1-1-2-2-2-211111-11-12211110000-1-1-1-1−i3−i3i3i3−i3−i3i3i300000000000000i3−i3i3−i30000000000
χ30222222-12222-1-1-1-2-2-2-2-1-1-2-2-22222-2-1-1-1-111-1-111-1-1-2-2-2-211111-11-12211110000-1-1-1-1i3i3−i3−i3i3i3−i3−i300000000000000−i3i3−i3i30000000000
χ312222-2-222-2-222220000-2-20002-2-22022-2-2002200222-22-200000-20-2002-22-20000000000000000000022−2−222−2−20000000000002−22−2
χ322222-2-222-2-222220000-2-20002-2-22022-2-2002200222-22-200000-20-2002-22-200000000000000000000−2−222−2−222000000000000−22−22
χ332222-2-222-2-222220000-2-20002-2-22022-2-200220022-22-2200000-20-200-22-220000000000000000000022−2−222−2−2000000000000−22−22
χ342222-2-222-2-222220000-2-20002-2-22022-2-200220022-22-2200000-20-200-22-2200000000000000000000−2−222−2−2220000000000002−22−2
χ352222-2-22-222-22220000-2-2-22-200002-2-222-2-200-2-2000000000020200000002−22−200002−22−22−22−222-2-22−22−22−22−20000000000000000
χ362222-2-22-222-22220000-2-2-22-200002-2-222-2-200-2-2000000000020200000002−22−200002−22−22−22−2-2-222−22−22−22−220000000000000000
χ372222-2-22-222-22220000-2-2-22-200002-2-222-2-200-2-200000000002020000000−22−220000−22−22−22−2222-2-2−22−22−22−220000000000000000
χ382222-2-22-222-22220000-2-2-22-200002-2-222-2-200-2-200000000002020000000−22−220000−22−22−22−22-2-2222−22−22−22−20000000000000000
χ3922-2-22-2222-2-22-2-200002-2-2-22000022-22-2-2-20022000000000020-20000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i22-2-22−i2i2−i2i2i2−i2i2−i20000000000000000
χ4022-2-22-2222-2-22-2-200002-2-2-22000022-22-2-2-20022000000000020-20000000−i2i2i2−i20000−i2i2−i2i2i2−i2i2−i2-222-2i2−i2i2−i2−i2i2−i2i20000000000000000
χ4122-2-22-2222-2-22-2-200002-2-2-22000022-22-2-2-20022000000000020-20000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i22-2-22i2−i2i2−i2−i2i2−i2i20000000000000000
χ4222-2-22-2222-2-22-2-200002-2-2-22000022-22-2-2-20022000000000020-20000000i2−i2−i2i20000i2−i2i2−i2−i2i2−i2i2-222-2−i2i2−i2i2i2−i2i2−i20000000000000000
χ4322-2-22-22-2-2222-2-200002-20002-22-20-22-22002200-2-22i−2i−2i2i00000-202002i−2i−2i2i00000000000000000000−i2−i2i2i2i2i2−i2−i2000000000000−222−2
χ4422-2-22-22-2-2222-2-200002-20002-22-20-22-22002200-2-22i−2i−2i2i00000-202002i−2i−2i2i00000000000000000000i2i2−i2−i2−i2−i2i2i20000000000002−2−22
χ4522-2-22-22-2-2222-2-200002-20002-22-20-22-22002200-2-2−2i2i2i−2i00000-20200−2i2i2i−2i00000000000000000000−i2−i2i2i2i2i2−i2−i20000000000002−2−22
χ4622-2-22-22-2-2222-2-200002-20002-22-20-22-22002200-2-2−2i2i2i−2i00000-20200−2i2i2i−2i00000000000000000000i2i2−i2−i2−i2−i2i2i2000000000000−222−2
χ4722-2-2-222-22-222-2-222-2-2-22-222-2-222-2-222-2-2-2-2-22222000022-2-2-2-22200000000000000000000000000000000000000002i−2i−2i2i000000
χ4822-2-2-222-22-222-2-222-2-2-22-222-2-222-2-222-2-2-2-2-22222000022-2-2-2-2220000000000000000000000000000000000000000−2i2i2i−2i000000
χ4922-2-2-222-22-222-2-2-2-222-222-2-2-2-2222-222-222-2-2-2-2220000-2-2222-2-2200000000000000000000002-22-2000000000000000000-220000
χ5022-2-2-222-22-222-2-2-2-222-222-2-2-2-2222-222-222-2-2-2-2220000-2-2222-2-220000000000000000000000-22-220000000000000000002-20000
χ5122-2-2-222-22-222-2-2-2-222-22-22222-2-2-2-222-2-2-22222-2-22i2i−2i−2i-2-222-222-2−2i2i2i2i−2i−2i0000−2i−2i2i2i000000000000000000000000000000000000
χ5222-2-2-222-22-222-2-2-2-222-22-22222-2-2-2-222-2-2-22222-2-2−2i−2i2i2i-2-222-222-22i−2i−2i−2i2i2i00002i2i−2i−2i000000000000000000000000000000000000
χ5322-2-2-22-1-22-22-11122-2-21-12-2-222-2-221-1-11-1-1-1-111112i2i−2i−2i-1-111-1-1112i−2i−i−iii2i2i−2i−2i−i−iii−i−i−i−iiiii0000000000002-2-1-1110000000000
χ5422-2-2-22-1-22-22-11122-2-21-12-2-222-2-221-1-11-1-1-1-111112i2i−2i−2i-1-111-1-1112i−2i−i−iii−2i−2i2i2i−i−iiiiiii−i−i−i−i000000000000-2211-1-10000000000
χ5522-2-2-22-1-22-22-11122-2-21-12-2-222-2-221-1-11-1-1-1-11111−2i−2i2i2i-1-111-1-111−2i2iii−i−i2i2i−2i−2iii−i−i−i−i−i−iiiii000000000000-2211-1-10000000000
χ5622-2-2-22-1-22-22-11122-2-21-12-2-222-2-221-1-11-1-1-1-11111−2i−2i2i2i-1-111-1-111−2i2iii−i−i−2i−2i2i2iii−i−iiiii−i−i−i−i0000000000002-2-1-1110000000000
χ5722-2-2-22-1-22-22-111-2-2221-1-22222-2-2-21-1-1111-1-1-1-1112i2i−2i−2i11-1-11-1-11−2i2i−i−iii0000ii−i−i33−3−3−3−33300000000000000−i3i3i3−i30000000000
χ5822-2-2-22-1-22-22-111-2-2221-1-22222-2-2-21-1-1111-1-1-1-1112i2i−2i−2i11-1-11-1-11−2i2i−i−iii0000ii−i−i−3−33333−3−300000000000000i3−i3−i3i30000000000
χ5922-2-2-22-1-22-22-111-2-2221-1-22222-2-2-21-1-1111-1-1-1-111−2i−2i2i2i11-1-11-1-112i−2iii−i−i0000−i−iii33−3−3−3−33300000000000000i3−i3−i3i30000000000
χ6022-2-2-22-1-22-22-111-2-2221-1-22222-2-2-21-1-1111-1-1-1-111−2i−2i2i2i11-1-11-1-112i−2iii−i−i0000−i−iii−3−33333−3−300000000000000−i3i3i3−i30000000000
χ614444444-4-4-4-444400004400000000-4-4-4-400000000000000000000000000000000000000000000002-2-222-2-220000000000000000
χ624444444-4-4-4-444400004400000000-4-4-4-40000000000000000000000000000000000000000000000-222-2-222-20000000000000000
χ63444444-24444-2-2-24444-2-2-4-4-4-4-4-4-4-4-2-2-2-2222222220000-2-2-2-2222200000000000000000000000000000000000000000000000000
χ64444444-24444-2-2-2-4-4-4-4-2-2444-4-4-4-44-2-2-2-2-2-222-2-22200002222-22-2200000000000000000000000000000000000000000000000000
χ654444-4-444-4-444440000-4-4000-444-4044-4-400-4-400-4-400000000040400000000000000000000000000000000000000000000000000
χ664444-4-44-444-44440000-4-44-440000-4-4-4444400440000000000-40-4000000000000000000000000000000000000000000000000000
χ674444-4-4-24-4-44-2-2-20000220004-4-440-2-22200-2-200-2-24-44-40000020200-22-2200000000000000000000000000000000000000000000
χ684444-4-4-24-4-44-2-2-20000220004-4-440-2-22200-2-200-2-2-44-4400000202002-22-200000000000000000000000000000000000000000000
χ694444-4-4-24-4-44-2-2-2000022000-444-40-2-22200220022000000000-20-2000000000023−2323−23000000000000000000000000000000000000
χ704444-4-4-24-4-44-2-2-2000022000-444-40-2-22200220022000000000-20-20000000000−2323−2323000000000000000000000000000000000000
χ714444-4-4-2-444-4-2-2-20000224-440000-422-2-2-2-200-2-20000000000202000000000000000i6−i6−i6i6i6−i6−i6i60000000000000000000000000000
χ724444-4-4-2-444-4-2-2-20000224-440000-422-2-2-2-200-2-20000000000202000000000000000−i6i6i6−i6−i6i6i6−i60000000000000000000000000000
χ734444-4-4-2-444-4-2-2-2000022-44-40000422-2-22200220000000000-20-2000000022−2222−220000−22−22−22−220000000000000000000000000000
χ744444-4-4-2-444-4-2-2-2000022-44-40000422-2-22200220000000000-20-20000000−2222−222200002−22−22−22−20000000000000000000000000000
χ7544-4-44-4444-4-44-4-400004-444-40000-44-44-44400-4-40000000000-404000000000000000000000000000000000000000000000000000
χ7644-4-44-44-4-4444-4-400004-4000-44-440-44-4400-4-4004400000000040-400000000000000000000000000000000000000000000000000
χ7744-4-44-4-244-4-4-2220000-2244-40000-4-22-22-2-20022000000000020-20000000000000006−6−66−666−60000000000000000000000000000
χ7844-4-44-4-244-4-4-2220000-2244-40000-4-22-22-2-20022000000000020-2000000000000000−666−66−6−660000000000000000000000000000
χ7944-4-44-4-244-4-4-2220000-22-4-4400004-22-222200-2-20000000000-2020000000−2i22i22i2−2i20000i2−i2i2−i2−i2i2−i2i20000000000000000000000000000
χ8044-4-44-4-244-4-4-2220000-22-4-4400004-22-222200-2-20000000000-20200000002i2−2i2−2i22i20000−i2i2−i2i2i2−i2i2−i20000000000000000000000000000
χ8144-4-44-4-2-4-444-2220000-220004-44-402-22-200-2-200224i−4i−4i4i0000020-200−2i2i2i−2i00000000000000000000000000000000000000000000
χ8244-4-44-4-2-4-444-2220000-220004-44-402-22-200-2-20022−4i4i4i−4i0000020-2002i−2i−2i2i00000000000000000000000000000000000000000000
χ8344-4-44-4-2-4-444-2220000-22000-44-4402-22-2002200-2-2000000000-2020000000000−2i32i32i3−2i3000000000000000000000000000000000000
χ8444-4-44-4-2-4-444-2220000-22000-44-4402-22-2002200-2-2000000000-20200000000002i3−2i3−2i32i3000000000000000000000000000000000000
χ8544-4-4-4444-44-44-4-40000-44000000004-4-4400000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ8644-4-4-4444-44-44-4-40000-44000000004-4-440000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ8744-4-4-44-2-44-44-22244-4-42-2-444-4-444-42-2-222222-2-2-2-20000-2-22222-2-200000000000000000000000000000000000000000000000000
χ8844-4-4-44-2-44-44-222-4-4442-24-4-4-4-44442-2-22-2-22222-2-2000022-2-2-222-200000000000000000000000000000000000000000000000000
χ89888888-4-8-8-8-8-4-4-40000-4-40000000044440000000000000000000000000000000000000000000000000000000000000000000000
χ9088-8-8-88-48-88-8-44400004-400000000-444-40000000000000000000000000000000000000000000000000000000000000000000000
χ918-88-80080000-88-84-44-4000000000000000000000000004-44-4000000000000000000000000000000000000000000000000000000
χ928-88-80080000-88-8-44-4400000000000000000000000000-44-44000000000000000000000000000000000000000000000000000000
χ938-88-800-400004-444-44-4000000000000002i6−2i62i6−2i62i6−2i62i6−2i60000-22-22000000000000000000000000000000000000000000000000000000
χ948-88-800-400004-444-44-400000000000000−2i62i6−2i62i6−2i62i6−2i62i60000-22-22000000000000000000000000000000000000000000000000000000
χ958-88-800-400004-44-44-44000000000000002i6−2i6−2i62i62i6−2i6−2i62i600002-22-2000000000000000000000000000000000000000000000000000000
χ968-88-800-400004-44-44-4400000000000000−2i62i62i6−2i6−2i62i62i6−2i600002-22-2000000000000000000000000000000000000000000000000000000
χ978-8-880080000-8-884-4-44000000000000000000000000004-4-44000000000000000000000000000000000000000000000000000000
χ988-8-880080000-8-88-444-400000000000000000000000000-444-4000000000000000000000000000000000000000000000000000000
χ998-8-8800-4000044-44-4-44000000000000002i6−2i62i6−2i6−2i62i6−2i62i60000-222-2000000000000000000000000000000000000000000000000000000
χ1008-8-8800-4000044-44-4-4400000000000000−2i62i6−2i62i62i6−2i62i6−2i60000-222-2000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4000044-4-444-4000000000000002i6−2i6−2i62i6−2i62i62i6−2i600002-2-22000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4000044-4-444-400000000000000−2i62i62i6−2i62i6−2i6−2i62i600002-2-22000000000000000000000000000000000000000000000000000000

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