Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#34312 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C2×C13×#548 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
2960 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(19,21)(22,23,28,26)(24,31,25,29)(27,34,35,30)(32,36,33,37);(22,24,28,25)(23,29,26,31)(27,32,35,33)(30,36,34,37);(18,19,20,21)(22,25,28,24)(23,29,26,31)(27,33,35,32)(30,36,34,37);(22,26,28,23)(24,29,25,31)(27,34,35,30)(32,36,33,37);(14,16,17,15)(22,27,28,35)(23,30,26,34)(24,32,25,33)(29,36,31,37)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27300);