Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1812 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C22×C42 |
| direct product | C13×#10866 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #117 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #380 |
| prime radical | C24×C13 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C22×C13×M16 ◁ G | |
746 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)(18,19)(20,28,31,24)(21,32)(22,35)(23,26)(25,33)(27,36)(29,42,44,46)(30,38,45,41)(34,47)(37,43,40,49)(39,48);(14,15,16,17)(18,20)(19,24)(21,29)(22,30)(23,31)(25,37)(26,28)(27,38)(32,46)(33,43)(34,44)(35,41)(36,45)(39,40)(42,47)(48,49);(18,21,22,33,23,34,36,48)(19,25,27,32,26,39,35,47)(20,29,30,43,31,44,45,49)(24,37,38,46,28,40,41,42)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3854);