Finite Group Databasebeta

← Group #13166016

Character table — Group #13166016

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size111122222222333344446666668888888888881212121216161616161616161616161618181818181824242424242424242424242424243636363636363636545454547272108108
order1222336666664444366644121212123336666666661212121233366666666622888812121212121212121212121212124466242424248888121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1
χ4111111111111-1-1-1-1111111-1-1-1-11111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511-1-111-1-1-111-111-1-11-1-111-111-1-1111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-11-1ii−i−i1-1111111-1-1-1-1-1-1i−i1-1ii−i−iii−i−ii−ii−i
χ611-1-111-1-1-111-111-1-11-1-111-111-1-1111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-11-1−i−iii1-1111111-1-1-1-1-1-1−ii1-1−i−iii−i−iii−ii−ii
χ711-1-111-1-1-111-1-1-1111-1-111-1-1-111111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1-11ii−i−i1-1-1-1-1-1-1-1111111i−i-11ii−i−i−i−iiii−i−ii
χ811-1-111-1-1-111-1-1-1111-1-111-1-1-111111-1-1-1-1-1-111111-1-1111111-1-1-1-1-1-1-11−i−iii1-1-1-1-1-1-1-1111111−ii-11−i−iiiii−i−i−iii−i
χ922222222222222222222222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122000022-1-1-1-1-1-1-1-1-1-1-1-10022000000000000
χ10222222222222-2-2-2-2222222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-2-200002211111111111100-2-2000000000000
χ1122222-12-1-12-122222-1-1-1-122-1-1-1-12-1-122-1-1-1-12-1-12-1-122-1-12-1-122-1-1-1-1220000-1-122-1-1-1-122-1-1-1-100-1-1000000000000
χ1222222-12-1-12-122222-1-1-1-122-1-1-1-1-12-1-1-122-1-1-12-12-1-12-12-1-12-1-1-122-1-1220000-1-1-1-122-1-1-1-122-1-100-1-1000000000000
χ1322222-12-1-12-122222-1-1-1-122-1-1-1-1-1-12-1-1-1-122-1-122-1-12-1-12-1-12-1-1-1-122220000-1-1-1-1-1-122-1-1-1-12200-1-1000000000000
χ1422222-12-1-12-12-2-2-2-2-1-1-1-12211112-1-122-1-1-1-12-1-12-1-122-1-12-1-122-1-1-1-1-2-20000-1-1-2-21111-2-211110011000000000000
χ1522222-12-1-12-12-2-2-2-2-1-1-1-1221111-12-1-1-122-1-1-12-12-1-12-12-1-12-1-1-122-1-1-2-20000-1-111-2-21111-2-2110011000000000000
χ1622222-12-1-12-12-2-2-2-2-1-1-1-1221111-1-12-1-1-1-122-1-122-1-12-1-12-1-12-1-1-1-122-2-20000-1-11111-2-21111-2-20011000000000000
χ172222-12-122-12-10000-1-1-1-1220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-1002222-1-10000000000002200-1-1-1-10000-1-100
χ182222-12-122-12-10000-1-1-1-1220000222222222222-122-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2-1-1000000000000-2-200111100001100
χ1922-2-222-2-2-222-222-2-22-2-222-222-2-2-1-1-1111111-1-1-122-2-2-1-1-1-1-1-11111112-200002-2-1-1-1-1-1-1111111002-2000000000000
χ2022-2-222-2-2-222-2-2-2222-2-222-2-2-222-1-1-1111111-1-1-122-2-2-1-1-1-1-1-1111111-2200002-2111111-1-1-1-1-1-100-22000000000000
χ2122-2-22-1-2112-1-222-2-2-111-12-2-1-1112-1-1-2-211112-1-12-11-22-1-12-1-1-2-211112-20000-1122-1-1-1-1-2-2111100-11000000000000
χ2222-2-22-1-2112-1-222-2-2-111-12-2-1-111-12-111-2-211-12-12-11-2-12-1-12-111-2-2112-20000-11-1-122-1-111-2-21100-11000000000000
χ2322-2-22-1-2112-1-222-2-2-111-12-2-1-111-1-121111-2-2-1-122-11-2-1-12-1-121111-2-22-20000-11-1-1-1-1221111-2-200-11000000000000
χ2422-2-22-1-2112-1-2-2-222-111-12-211-1-12-1-1-2-211112-1-12-11-22-1-12-1-1-2-21111-220000-11-2-2111122-1-1-1-1001-1000000000000
χ2522-2-22-1-2112-1-2-2-222-111-12-211-1-1-12-111-2-211-12-12-11-2-12-1-12-111-2-211-220000-1111-2-211-1-122-1-1001-1000000000000
χ2622-2-22-1-2112-1-2-2-222-111-12-211-1-1-1-121111-2-2-1-122-11-2-1-12-1-121111-2-2-220000-111111-2-2-1-1-1-122001-1000000000000
χ2722-2-2-121-2-2-1210000-111-12-20000222-2-2-2-2-2-2222-12-21-1-1-1-1-1-1111111002i2i−2i−2i-110000000000002i−2i00−i−iii0000−ii00
χ2822-2-2-121-2-2-1210000-111-12-20000222-2-2-2-2-2-2222-12-21-1-1-1-1-1-111111100−2i−2i2i2i-11000000000000−2i2i00ii−i−i0000i−i00
χ292-22-222-22-2-2-222i−2i2i−2i22-2-2002i−2i2i−2i-1-1-11-11-11-11110000-1-1-11111-11-11-100i2−i2i2−i200i−ii−ii−ii−ii−ii−i0000i2−i2i2−i22−22−20000
χ302-22-222-22-2-2-222i−2i2i−2i22-2-2002i−2i2i−2i-1-1-11-11-11-11110000-1-1-11111-11-11-100−i2i2−i2i200i−ii−ii−ii−ii−ii−i0000−i2i2−i2i2−22−220000
χ312-22-222-22-2-2-22−2i2i−2i2i22-2-200−2i2i−2i2i-1-1-11-11-11-11110000-1-1-11111-11-11-100i2−i2i2−i200−ii−ii−ii−ii−ii−ii0000i2−i2i2−i2−22−220000
χ322-22-222-22-2-2-22−2i2i−2i2i22-2-200−2i2i−2i2i-1-1-11-11-11-11110000-1-1-11111-11-11-100−i2i2−i2i200−ii−ii−ii−ii−ii−ii0000−i2i2−i2i22−22−20000
χ332-2-22222-22-2-2-22i−2i−2i2i2-22-2002i−2i−2i2i-1-1-1-11-11-111110000-1-1-1111-11-11-11002−2−2200i−ii−ii−i−ii−ii−ii00002−2−22−i2i2i2−i20000
χ342-2-22222-22-2-2-22i−2i−2i2i2-22-2002i−2i−2i2i-1-1-1-11-11-111110000-1-1-1111-11-11-1100−222−200i−ii−ii−i−ii−ii−ii0000−222−2i2−i2−i2i20000
χ352-2-22222-22-2-2-2−2i2i2i−2i2-22-200−2i2i2i−2i-1-1-1-11-11-111110000-1-1-1111-11-11-11002−2−2200−ii−ii−iii−ii−ii−i00002−2−22i2−i2−i2i20000
χ362-2-22222-22-2-2-2−2i2i2i−2i2-22-200−2i2i2i−2i-1-1-1-11-11-111110000-1-1-1111-11-11-1100−222−200−ii−ii−iii−ii−ii−i0000−222−2−i2i2i2−i20000
χ3733333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-11111-1-1000000000000-1-1-1-111111111-1-1-1-1
χ3833333333333333333333-1-13333000000000000-1-1-1-1000000000000-1-1-1-1-1-1-1-100000000000011-1-1-1-1-1-1-1-1-1-11111
χ39333333333333-3-3-3-33333-1-1-3-3-3-3000000000000-1-1-1-1000000000000111111-1-1000000000000-1-1111111-1-1-1-1-1-111
χ40333333333333-3-3-3-33333-1-1-3-3-3-3000000000000-1-1-1-100000000000011-1-1-1-1-1-10000000000001111-1-1-1-1111111-1-1
χ4133-3-333-3-3-333-333-3-33-3-33-1133-3-3000000000000-1-111000000000000-11ii−i−i-11000000000000−ii-11ii−i−iii−i−i−ii−ii
χ4233-3-333-3-3-333-333-3-33-3-33-1133-3-3000000000000-1-111000000000000-11−i−iii-11000000000000i−i-11−i−iii−i−iiii−ii−i
χ4333-3-333-3-3-333-3-3-3333-3-33-11-3-333000000000000-1-1110000000000001-1ii−i−i-11000000000000−ii1-1ii−i−i−i−iii−iii−i
χ4433-3-333-3-3-333-3-3-3333-3-33-11-3-333000000000000-1-1110000000000001-1−i−iii-11000000000000i−i1-1−i−iiiii−i−ii−i−ii
χ454444-24-244-24-20000-2-2-2-2440000-2-2-2-2-2-2-2-2-2-2-2-2-244-2111111111111000000-2-20000000000000000000000000000
χ464444-2-2-2-2-2-2-2-2000011114400004-2-244-2-2-2-24-2-2-2-2-2-2-211-211-2-21111000000110000000000000000000000000000
χ474444-2-2-2-2-2-2-2-200001111440000-24-2-2-244-2-2-24-2-2-2-2-21-211-2111-2-211000000110000000000000000000000000000
χ484444-2-2-2-2-2-2-2-200001111440000-2-24-2-2-2-244-2-24-2-2-2-211-211-21111-2-2000000110000000000000000000000000000
χ4944-4-4-242-4-4-2420000-222-24-40000-2-2-2222222-2-2-2-24-42111111-1-1-1-1-1-1000000-220000000000000000000000000000
χ5044-4-4-2-2222-2-2200001-1-114-400004-2-2-4-422224-2-2-2-222-211-21122-1-1-1-10000001-10000000000000000000000000000
χ5144-4-4-2-2222-2-2200001-1-114-40000-24-222-4-422-24-2-2-2221-211-21-1-122-1-10000001-10000000000000000000000000000
χ5244-4-4-2-2222-2-2200001-1-114-40000-2-242222-4-4-2-24-2-22211-211-2-1-1-1-1220000001-10000000000000000000000000000
χ534-44-444-44-4-4-444i−4i4i−4i44-4-4004i−4i4i−4i111-11-11-11-1-1-10000111-1-1-1-11-11-1100000000−ii−ii−ii−ii−ii−ii0000000000000000
χ544-44-444-44-4-4-44−4i4i−4i4i44-4-400−4i4i−4i4i111-11-11-11-1-1-10000111-1-1-1-11-11-1100000000i−ii−ii−ii−ii−ii−i0000000000000000
χ554-44-44-2-4-22-4244i−4i4i−4i-2-22200−2i2i−2i2i11-2-11-112-2-1-12000011-2-1-12-11-112-200000000−ii−ii2i−2i−ii−ii2i−2i0000000000000000
χ564-44-44-2-4-22-4244i−4i4i−4i-2-22200−2i2i−2i2i1-21-112-2-11-12-100001-21-12-1-112-2-1100000000−ii2i−2i−ii−ii2i−2i−ii0000000000000000
χ574-44-44-2-4-22-4244i−4i4i−4i-2-22200−2i2i−2i2i-2112-2-11-112-1-10000-2112-1-12-2-11-11000000002i−2i−ii−ii2i−2i−ii−ii0000000000000000
χ584-44-44-2-4-22-424−4i4i−4i4i-2-222002i−2i2i−2i11-2-11-112-2-1-12000011-2-1-12-11-112-200000000i−ii−i−2i2ii−ii−i−2i2i0000000000000000
χ594-44-44-2-4-22-424−4i4i−4i4i-2-222002i−2i2i−2i1-21-112-2-11-12-100001-21-12-1-112-2-1100000000i−i−2i2ii−ii−i−2i2ii−i0000000000000000
χ604-44-44-2-4-22-424−4i4i−4i4i-2-222002i−2i2i−2i-2112-2-11-112-1-10000-2112-1-12-2-11-1100000000−2i2ii−ii−i−2i2ii−ii−i0000000000000000
χ614-44-4-2424-42-4-20000-2-222000000-2-2-22-22-22-22220000111-1-1-1-11-11-11002i2−2i22i2−2i2000000000000000000−i2i2−i2i200000000
χ624-44-4-2424-42-4-20000-2-222000000-2-2-22-22-22-22220000111-1-1-1-11-11-1100−2i22i2−2i22i2000000000000000000i2−i2i2−i200000000
χ634-4-44444-44-4-4-44i−4i−4i4i4-44-4004i−4i−4i4i1111-11-11-1-1-1-10000111-1-1-11-11-11-100000000−ii−ii−iii−ii−ii−i0000000000000000
χ644-4-44444-44-4-4-4−4i4i4i−4i4-44-400−4i4i4i−4i1111-11-11-1-1-1-10000111-1-1-11-11-11-100000000i−ii−ii−i−ii−ii−ii0000000000000000
χ654-4-444-242-2-42-44i−4i−4i4i-22-2200−2i2i2i−2i11-21-11-1-22-1-12000011-2-1-121-11-1-2200000000−ii−ii2i−2ii−ii−i−2i2i0000000000000000
χ664-4-444-242-2-42-44i−4i−4i4i-22-2200−2i2i2i−2i1-211-1-221-1-12-100001-21-12-11-1-221-100000000−ii2i−2i−iii−i−2i2ii−i0000000000000000
χ674-4-444-242-2-42-44i−4i−4i4i-22-2200−2i2i2i−2i-211-221-11-12-1-10000-2112-1-1-221-11-1000000002i−2i−ii−ii−2i2ii−ii−i0000000000000000
χ684-4-444-242-2-42-4−4i4i4i−4i-22-22002i−2i−2i2i11-21-11-1-22-1-12000011-2-1-121-11-1-2200000000i−ii−i−2i2i−ii−ii2i−2i0000000000000000
χ694-4-444-242-2-42-4−4i4i4i−4i-22-22002i−2i−2i2i1-211-1-221-1-12-100001-21-12-11-1-221-100000000i−i−2i2ii−i−ii2i−2i−ii0000000000000000
χ704-4-444-242-2-42-4−4i4i4i−4i-22-22002i−2i−2i2i-211-221-11-12-1-10000-2112-1-1-221-11-100000000−2i2ii−ii−i2i−2i−ii−ii0000000000000000
χ714-4-44-24-2-442-420000-22-22000000-2-2-2-22-22-222220000111-1-1-11-11-11-10022−22−2222000000000000000000−222−200000000
χ724-4-44-24-2-442-420000-22-22000000-2-2-2-22-22-222220000111-1-1-11-11-11-100−222222−220000000000000000002−2−2200000000
χ7366666-36-3-36-366666-3-3-3-3-2-2-3-3-3-3000000000000-211-2000000000000-2-20000110000000000000011000000000000
χ7466666-36-3-36-36-6-6-6-6-3-3-3-3-2-23333000000000000-211-20000000000002200001100000000000000-1-1000000000000
χ756666-36-366-36-30000-3-3-3-3-2-200000000000000001-2-2100000000000000222211000000000000-2-200-1-1-1-100001100
χ766666-36-366-36-30000-3-3-3-3-2-200000000000000001-2-2100000000000000-2-2-2-211000000000000220011110000-1-100
χ7766-6-66-3-6336-3-666-6-6-333-3-22-3-333000000000000-21-12000000000000-2200001-1000000000000001-1000000000000
χ7866-6-66-3-6336-3-6-6-666-333-3-2233-3-3000000000000-21-120000000000002-200001-100000000000000-11000000000000
χ7966-6-6-363-6-6-3630000-333-3-2200000000000000001-22-1000000000000002i2i−2i−2i1-1000000000000−2i2i00−i−iii0000i−i00
χ8066-6-6-363-6-6-3630000-333-3-2200000000000000001-22-100000000000000−2i−2i2i2i1-10000000000002i−2i00ii−i−i0000−ii00
χ818-88-8-4848-84-8-40000-4-444000000222-22-22-22-2-2-20000-1-1-11111-11-11-1000000000000000000000000000000000000
χ828-88-8-4-44-4444-4000022-2-200000022-4-22-224-4-2-240000-1-1211-21-11-1-22000000000000000000000000000000000000
χ838-88-8-4-44-4444-4000022-2-20000002-42-224-4-22-24-20000-12-11-211-1-221-1000000000000000000000000000000000000
χ848-88-8-4-44-4444-4000022-2-2000000-4224-4-22-224-2-200002-1-1-211-221-11-1000000000000000000000000000000000000
χ858-8-88-48-4-884-840000-44-440000002222-22-22-2-2-2-20000-1-1-1111-11-11-11000000000000000000000000000000000000
χ868-8-88-4-4-44-444400002-22-200000022-42-22-2-44-2-240000-1-1211-2-11-112-2000000000000000000000000000000000000
χ878-8-88-4-4-44-444400002-22-20000002-422-2-442-2-24-20000-12-11-21-112-2-11000000000000000000000000000000000000
χ888-8-88-4-4-44-444400002-22-2000000-422-442-22-24-2-200002-1-1-2112-2-11-11000000000000000000000000000000000000
χ8912121212-6-6-6-6-6-6-6-600003333-4-400000000000000002222000000000000000000-1-10000000000000000000000000000
χ901212-12-12-6-6666-6-6600003-3-33-44000000000000000022-2-2000000000000000000-110000000000000000000000000000

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