Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12606 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×C42 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C22×C13 | C2×#97 |
| prime radical | C24×C13 | M16 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ G | |
466 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)(20,30,32,39)(21,27)(22,36)(23,29)(24,26)(25,31,40,34)(28,37)(33,47,46,44)(35,43)(38,42)(41,48,49,45);(15,17)(18,20,22,33,23,34,38,48,24,32,37,46,21,31,35,45)(19,25,28,41,29,39,43,47,26,40,36,49,27,30,42,44);(19,26)(20,31,32,34)(22,37)(25,39,40,30)(27,29)(33,48,46,45)(35,38)(41,44,49,47)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5594);