Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12608 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | #432 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C2×C13×#97 ◁ G | |
462 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,30,33,41)(21,27)(22,28)(23,29)(24,26)(25,32,38,31)(34,44,47,49)(35,42)(36,40)(37,43)(39,46,48,45);(15,17)(18,20,22,34,23,32,37,46,24,33,36,47,21,31,35,45)(19,25,28,39,29,30,43,44,26,38,40,48,27,41,42,49);(19,26)(20,31,33,32)(22,36)(25,30,38,41)(27,29)(34,46,47,45)(35,37)(39,49,48,44)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5596);