Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#8319 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C2×C4 | C22×C8×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| socle | C22×C13 | #379 |
| prime radical | C2×C13×2−1+4 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C42×C13 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,18,17,19,20,21)(23,27)(25,32)(28,36)(29,33)(30,34)(35,37);(22,23)(24,28)(25,33)(26,29)(27,32)(30,35)(31,37)(34,36);(22,24,26,31)(23,28,29,37)(25,34,32,30)(27,35,33,36)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 1307);