Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#34211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
3102 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 5 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,21,20)(22,23)(24,25)(26,34)(27,28)(29,32)(30,35)(31,36)(33,37);(18,20,21,19)(23,28)(25,29)(30,34)(33,36);(14,15,16,17)(22,24)(23,29)(25,28)(26,31)(27,32)(30,36)(33,34)(35,37);(22,25,27,29)(23,24,28,32)(26,33,35,36)(30,31,34,37);(22,26,27,35)(23,30,28,34)(24,31,32,37)(25,33,29,36)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27199);