Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12725 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#12726 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #1782 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C13×#534 | C22 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C23×C13 ◁ C13×#518 ◁ G | |
708 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)(18,31,32,22)(19,23)(20,26,34,41)(21,30)(25,38)(27,37)(29,35,44,43)(33,45,42,39)(36,40);(14,16,19,27)(15,20,23,34)(17,25,30,40)(18,26,32,41)(21,33,28,42)(22,24,31,37)(29,39,44,45)(35,36,43,38);(14,17)(15,21,23,28)(16,25)(18,29)(19,30)(20,33,34,42)(22,35,31,43)(24,36,37,38)(26,39)(27,40)(32,44)(41,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5714);