Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #63041 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C13 · Schur multiplier (H2) = C213 |
| direct product | C13×#63057 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ G | |
6180 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 6 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(17,25)(20,22)(23,29)(31,36)(37,47)(38,48)(39,49)(50,58)(51,59)(52,53)(60,61);(14,15,18,19)(16,22,24,20)(17,21,25,26)(23,28,29,27)(31,36)(32,40)(38,48)(39,49)(41,54)(42,55)(52,53)(56,57);(14,16,18,24)(15,20,19,22)(17,23,25,29)(21,27,26,28)(30,31)(32,37)(33,38)(34,39)(35,36)(40,47)(41,50)(42,51)(43,52)(44,48)(45,53)(46,49)(54,58)(55,59)(56,60)(57,61);(14,17)(15,21)(16,23)(18,25)(19,26)(20,27)(22,28)(24,29)(30,32)(31,37)(33,41)(34,42)(35,40)(36,47)(38,50)(39,51)(43,56)(44,54)(45,57)(46,55)(48,58)(49,59)(52,60)(53,61);(30,33,35,44)(31,38,36,48)(32,41,40,54)(34,45,46,43)(37,50,47,58)(39,53,49,52)(42,57,55,56)(51,61,59,60);(30,34,35,46)(31,39,36,49)(32,42,40,55)(33,43,44,45)(37,51,47,59)(38,52,48,53)(41,56,54,57)(50,60,58,61)910 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 56045);