Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C13 · Schur multiplier (H2) = C2×C43 |
| direct product | C13×#13780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator | C22 | C22×C42×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| prime radical | C25×C13 | C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
1710 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(18,19,21,20)(23,26)(27,29)(30,31,33,34)(32,36,37,35);(14,15,16,17)(18,20,21,19)(31,34)(35,36);(22,23)(24,27)(25,26)(28,29)(30,31)(32,35)(33,34)(36,37);(22,24,25,28)(23,27,26,29)(30,32,33,37)(31,35,34,36)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6768);