Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11522 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12806 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #410 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×#41 | C23×C13 |
| socle | C2×C13 | #1799 |
| prime radical | C13×#525 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C2×C8×C13 ◁ C2×C13×#131 ◁ G | |
420 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,24)(17,28)(18,31,32,21)(19,23)(20,26)(22,30)(25,39)(27,37,41,38)(29,36,44,43)(33,45,34,42)(35,40);(14,16,17,26,19,25,30,40)(15,20,22,24,23,35,28,39)(18,27,29,42,32,41,44,45)(21,34,36,38,31,33,43,37);(15,21)(16,25)(20,33)(22,36)(23,31)(24,37)(26,40)(27,41)(28,43)(34,35)(38,39)(42,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5794);