Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #3415 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33454 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C2×C13×#509 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#117 ◁ C13×#405 ◁ G | |
696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,25)(21,24)(22,35)(23,28)(26,32)(27,33)(29,39)(30,36)(31,45)(34,38)(37,46)(40,44)(41,43)(42,47)(48,49);(19,24)(21,32)(22,33)(25,36)(26,27)(28,38)(30,44)(31,43)(34,46)(35,37)(39,47)(40,41)(42,49)(45,48);(14,16,17,15)(18,20)(19,25)(21,30)(22,31)(23,29)(24,36)(26,40)(27,41)(28,39)(32,44)(33,43)(34,42)(35,45)(37,48)(38,47)(46,49);(20,29)(25,39)(30,42)(31,43)(36,47)(40,48)(41,45)(44,49)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26442);