Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#8964 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C22×D4×C13 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
542 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,20,17,16,19,21)(22,23)(24,32,35,36)(25,29,28,34)(26,30)(27,31)(33,37);(14,16,18,21,17,15,19,20)(22,24,33,34,27,35,26,29)(23,28,37,32,31,25,30,36);(15,16)(20,21)(22,25,27,28)(23,29,31,34)(24,30,35,37)(26,32,33,36)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1952);