Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C13 · Schur multiplier (H2) = C210 |
| direct product | C13×#34171 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C25 |
| commutator | C22 | C24×C4×C13 |
| Frattini, cosocle | C23 | C25×C13 |
| prime radical | C24×D4×C13 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ G | |
7734 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,20,21)(22,23)(24,28)(25,26)(27,29);(23,26)(27,28);(14,15)(16,17)(18,19)(20,21);(22,23)(24,27)(25,26)(28,29);(22,24)(23,27)(25,29)(26,28)1144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 27159);