Finite Group Databasebeta

← Group #13165183

Character table — Group #13165183

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78
size1111222244444444668888888812121212181818181818242424242424242424242424242424242424242427272727363636363636363636365454545472727272
order1244361212336612121212883366121212122244248888666666661212121212121212242424248888688881224242424444424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-11-111-1-1-1-11-11-111-1-11-11-111-1-111111111111-1-11-1-1-1-1-1-1-1-111-1-1
χ311111111111111111111111111-11-1111-1-1-1-1-11-11-1-111-11-11-1-111111111111-1-1111-1-1-1-1-1-1-1-1-1-111
χ411111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111-1-1-1-1
χ51111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1111111111-11-111-1-1-1-11-11-111-1-11-11-111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-11111-1-111
χ71111111111111111-1-111111111-11-1111-1-1-1-1-11-11-1-111-11-11-1-111-1-1-1-1-1-1-1-1111-1-11-1-1-1-1111111-1-1
χ81111111111111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111
χ911-1-111-1-11111-1-1-1-1i−i1111-1-1-1-111-1-1-1111-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i-1i−ii−i111-1-1ii−i−ii−ii−i
χ1011-1-111-1-11111-1-1-1-1i−i1111-1-1-1-11-1-11-11-1-1111-11-111-1-1-11-11-1-111ii−i−iii−i−i-1i−i−ii1-1-111−i−iiii−i−ii
χ1111-1-111-1-11111-1-1-1-1i−i1111-1-1-1-1-111-1-11-1-111-11-11-1-1111-11-111-1-1ii−i−iii−i−i-1−iii−i1-1-111−i−iii−iii−i
χ1211-1-111-1-11111-1-1-1-1i−i1111-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-1-111111111ii−i−iii−i−i-1−ii−ii111-1-1ii−i−i−ii−ii
χ1311-1-111-1-11111-1-1-1-1−ii1111-1-1-1-111-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii-1−ii−ii111-1-1−i−iii−ii−ii
χ1411-1-111-1-11111-1-1-1-1−ii1111-1-1-1-11-1-11-11-1-1111-11-111-1-1-11-11-1-111−i−iii−i−iii-1−iii−i1-1-111ii−i−i−iii−i
χ1511-1-111-1-11111-1-1-1-1−ii1111-1-1-1-1-111-1-11-1-111-11-11-1-1111-11-111-1-1−i−iii−i−iii-1i−i−ii1-1-111ii−i−ii−i−ii
χ1611-1-111-1-11111-1-1-1-1−ii1111-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-1-111111111−i−iii−i−iii-1i−ii−i111-1-1−i−iiii−ii−i
χ17222222222222222222222222220000-2-2000000000000000000002222-2-2-2-2-20000-2000000000000
χ182222222222222222-2-2222222220000-2-200000000000000000000-2-2-2-22222-20000-2000000000000
χ192222-1-1-1-12222222200-1-1-1-1-1-1-1-12222222222-1-122-1-1-1-1-1-122-1-1-1-100000000-10000-1-1-1-1-100000000
χ202222-1-1-1-12222222200-1-1-1-1-1-1-1-12-22-222-2-2-2-2-112-2-1-111-112-2-1-11100000000-10000-1111100000000
χ212222-1-1-1-12222222200-1-1-1-1-1-1-1-1-22-2222-2-2-2-21-1-2211-1-11-1-2211-1-100000000-10000-1111100000000
χ222222-1-1-1-12222222200-1-1-1-1-1-1-1-1-2-2-2-222222211-2-2111111-2-2111100000000-10000-1-1-1-1-100000000
χ2322-2-222-2-22222-2-2-2-22i−2i2222-2-2-2-200002-2000000000000000000002i2i−2i−2i−2i−2i2i2i20000-2000000000000
χ2422-2-222-2-22222-2-2-2-2−2i2i2222-2-2-2-200002-200000000000000000000−2i−2i2i2i2i2i−2i−2i20000-2000000000000
χ2522-2-2-1-1112222-2-2-2-200-1-1-1-1111122-2-2-2222-2-2-1-122-1-1-1-111-2-211110000000010000-1-1-11100000000
χ2622-2-2-1-1112222-2-2-2-200-1-1-1-111112-2-22-22-2-222-112-2-1-1111-1-2211-1-10000000010000-111-1-100000000
χ2722-2-2-1-1112222-2-2-2-200-1-1-1-11111-222-2-22-2-2221-1-2211-1-1-112-2-1-1110000000010000-111-1-100000000
χ2822-2-2-1-1112222-2-2-2-200-1-1-1-11111-2-222-2222-2-211-2-21111-1-122-1-1-1-10000000010000-1-1-11100000000
χ292-22i−2i2-22i−2i22-2-22i2i−2i−2i0022-2-22i2i−2i−2i0000002−2i2−i2000000000000000000002ζ3−2ζ32ζ−2ζ0000002−2i2−i21−i−1+i1+i−1−i0000
χ302-22i−2i2-22i−2i22-2-22i2i−2i−2i0022-2-22i2i−2i−2i0000002−2i2−i200000000000000000000−2ζ32ζ3−2ζ2ζ0000002−2i2−i2−1+i1−i−1−i1+i0000
χ312-22i−2i2-22i−2i22-2-22i2i−2i−2i0022-2-22i2i−2i−2i000000−22−i2i2000000000000000000002ζ3−2ζ32ζ−2ζ000000−22−i2i2−1+i1−i−1−i1+i0000
χ322-22i−2i2-22i−2i22-2-22i2i−2i−2i0022-2-22i2i−2i−2i000000−22−i2i200000000000000000000−2ζ32ζ3−2ζ2ζ000000−22−i2i21−i−1+i1+i−1−i0000
χ332-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i0022-2-2−2i−2i2i2i0000002−2−i2i2000000000000000000002ζ−2ζ2ζ3−2ζ30000002−2−i2i2−1−i1+i−1+i1−i0000
χ342-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i0022-2-2−2i−2i2i2i0000002−2−i2i200000000000000000000−2ζ2ζ−2ζ32ζ30000002−2−i2i21+i−1−i1−i−1+i0000
χ352-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i0022-2-2−2i−2i2i2i000000−22i2−i2000000000000000000002ζ−2ζ2ζ3−2ζ3000000−22i2−i21+i−1−i1−i−1+i0000
χ362-2−2i2i2-2−2i2i22-2-2−2i−2i2i2i0022-2-2−2i−2i2i2i000000−22i2−i200000000000000000000−2ζ2ζ−2ζ32ζ3000000−22i2−i2−1−i1+i−1+i1−i0000
χ37444444441-21-21-21-2441-21-21-21-20202000000020-100-1-1020-100-1-11-21-200000002200000000000-1-1
χ38444444441-21-21-21-2441-21-21-21-20-20-20000000-20100110-20100111-21-20000000-2-20000000000011
χ39444444441-21-21-21-2-4-41-21-21-21-20202000000020-100-1-1020-100-1-1-12-120000000-2-20000000000011
χ40444444441-21-21-21-2-4-41-21-21-21-20-20-20000000-20100110-2010011-12-1200000002200000000000-1-1
χ4144444444-21-21-21-2144-21-21-21-21202000000020-10-1-10020-10-1-100-21-21000002200000000000-1-100
χ4244444444-21-21-21-2144-21-21-21-21-20-20000000-20101100-20101100-21-2100000-2-2000000000001100
χ4344444444-21-21-21-21-4-4-21-21-21-21202000000020-10-1-10020-10-1-1002-12-100000-2-2000000000001100
χ4444444444-21-21-21-21-4-4-21-21-21-21-20-20000000-20101100-201011002-12-1000002200000000000-1-100
χ454444-2-2-2-24444444400-2-2-2-2-2-2-2-20000-4-40000000000000000000000000000200002000000000000
χ4644-4-444-4-41-21-2-12-124i−4i1-21-2-12-12020-2000000020-100-1-10-2010011i−2i−i2i00000002i−2i00000000000−ii
χ4744-4-444-4-41-21-2-12-124i−4i1-21-2-12-120-2020000000-2010011020-100-1-1i−2i−i2i0000000−2i2i00000000000i−i
χ4844-4-444-4-41-21-2-12-12−4i4i1-21-2-12-12020-2000000020-100-1-10-2010011−i2ii−2i0000000−2i2i00000000000i−i
χ4944-4-444-4-41-21-2-12-12−4i4i1-21-2-12-120-2020000000-2010011020-100-1-1−i2ii−2i00000002i−2i00000000000−ii
χ5044-4-444-4-4-21-212-12-14i−4i-21-212-12-120-2000000020-10-1-100-20101100−2ii2i−i000002i−2i00000000000−ii00
χ5144-4-444-4-4-21-212-12-14i−4i-21-212-12-1-2020000000-2010110020-10-1-100−2ii2i−i00000−2i2i00000000000i−i00
χ5244-4-444-4-4-21-212-12-1−4i4i-21-212-12-120-2000000020-10-1-100-201011002i−i−2ii00000−2i2i00000000000i−i00
χ5344-4-444-4-4-21-212-12-1−4i4i-21-212-12-1-2020000000-2010110020-10-1-1002i−i−2ii000002i−2i00000000000−ii00
χ5444-4-4-2-2224444-4-4-4-400-2-2-2-2222200004-40000000000000000000000000000-200002000000000000
χ554-44i−4i-22−2i2i44-4-44i4i−4i−4i00-2-222−2i−2i2i2i00000022−222i2−2i2000000000000000000000000000000−22−i2i200000000
χ564-44i−4i-22−2i2i44-4-44i4i−4i−4i00-2-222−2i−2i2i2i000000−2222−2i22i20000000000000000000000000000002−2i2−i200000000
χ574-4−4i4i-222i−2i44-4-4−4i−4i4i4i00-2-2222i2i−2i−2i00000022−22−2i22i2000000000000000000000000000000−22i2−i200000000
χ584-4−4i4i-222i−2i44-4-4−4i−4i4i4i00-2-2222i2i−2i−2i000000−22222i2−2i20000000000000000000000000000002−2−i2i200000000
χ598888-4-4-4-42-42-42-42-400-12-12-12-1204040000000-20-200110-20-2001100000000000000000000000000
χ608888-4-4-4-42-42-42-42-400-12-12-12-120-40-4000000020200-1-1020200-1-100000000000000000000000000
χ618888-4-4-4-4-42-42-42-42002-12-12-12-14040000000-20-201100-20-20110000000000000000000000000000
χ628888-4-4-4-4-42-42-42-42002-12-12-12-1-40-400000002020-1-1002020-1-10000000000000000000000000000
χ6388-8-8-4-4442-42-4-24-2400-12-121-21-2040-40000000-20-20011020200-1-100000000000000000000000000
χ6488-8-8-4-4442-42-4-24-2400-12-121-21-20-404000000020200-1-10-20-2001100000000000000000000000000
χ6588-8-8-4-444-42-424-24-2002-12-1-21-2140-40000000-20-2011002020-1-10000000000000000000000000000
χ6688-8-8-4-444-42-424-24-2002-12-1-21-21-40400000002020-1-100-20-20110000000000000000000000000000
χ678-88i−8i8-88i−8i2-4-242i−4i−2i4i002-4-242i−4i−2i4i0000000000000000000000000000000000000000000000000000
χ688-88i−8i8-88i−8i-424-2−4i2i4i−2i00-424-2−4i2i4i−2i0000000000000000000000000000000000000000000000000000
χ698-88i−8i-44−4i4i2-4-242i−4i−2i4i00-121-2−i2ii−2i00000000000000003-30000003i−3i00000000000000000000000000
χ708-88i−8i-44−4i4i2-4-242i−4i−2i4i00-121-2−i2ii−2i0000000000000000-33000000−3i3i00000000000000000000000000
χ718-88i−8i-44−4i4i-424-2−4i2i4i−2i002-1-212i−i−2ii000000000000003-30000003i−3i0000000000000000000000000000
χ728-88i−8i-44−4i4i-424-2−4i2i4i−2i002-1-212i−i−2ii00000000000000-33000000−3i3i0000000000000000000000000000
χ738-8−8i8i8-8−8i8i2-4-24−2i4i2i−4i002-4-24−2i4i2i−4i0000000000000000000000000000000000000000000000000000
χ748-8−8i8i8-8−8i8i-424-24i−2i−4i2i00-424-24i−2i−4i2i0000000000000000000000000000000000000000000000000000
χ758-8−8i8i-444i−4i2-4-24−2i4i2i−4i00-121-2i−2i−i2i00000000000000003-3000000−3i3i00000000000000000000000000
χ768-8−8i8i-444i−4i2-4-24−2i4i2i−4i00-121-2i−2i−i2i0000000000000000-330000003i−3i00000000000000000000000000
χ778-8−8i8i-444i−4i-424-24i−2i−4i2i002-1-21−2ii2i−i000000000000003-3000000−3i3i0000000000000000000000000000
χ788-8−8i8i-444i−4i-424-24i−2i−4i2i002-1-21−2ii2i−i00000000000000-330000003i−3i0000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.