Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C13 · Schur multiplier (H2) = C2×C4 |
| direct product | C13×#12654 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C13 | C23 |
| commutator | C22 | C2×C4×C8×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle, prime radical | C23×C13 | C22×C8 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C13 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(18,19,21,20)(22,23)(24,28)(25,30)(26,31)(27,29)(32,39)(33,40)(34,38)(35,43)(36,41)(37,42)(44,50)(45,48)(46,49)(47,51)(52,53);(15,17)(22,24,25,32,26,33,35,44,27,34,36,45,37,46,47,52)(23,28,30,39,31,40,43,50,29,38,41,48,42,49,51,53);(18,20,21,19)(23,29)(28,38)(30,41)(31,42)(39,48)(40,49)(43,51)(50,53)1456 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5642);