Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C24×C4 |
| direct product | C13×#20505 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C22×D4 |
| commutator | C4 | C22×C42×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C13×#376 ◁ G | |
1054 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(22,23,26,30)(24,28,31,35)(25,27,33,29)(32,34,37,36);(18,19,21,20)(23,27)(25,33)(28,34)(29,30)(32,37)(35,36);(18,20,21,19)(22,24,26,31)(23,28,30,35)(25,32,33,37)(27,34,29,36);(14,16,17,15)(24,31)(28,35)(32,37)(34,36)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13493);