Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13027 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #459 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| socle | C2×C13 | #1879 |
| prime radical | C13×#3414 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C2×C4×C8×C13 ◁ G | |
484 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)(14,15,19,24,20,26,37,44,21,27,17,34,36,39,18,25)(16,28,31,41,32,40,30,42,33,45,29,23,38,43,35,22);(14,16)(15,22,27,42)(17,35)(18,29)(19,30)(20,38)(21,33)(23,39,41,26)(24,40,34,43)(25,45,44,28)(31,37)(32,36);(14,16)(15,23)(17,35)(18,29)(19,30)(20,38)(21,33)(22,39)(24,28)(25,40)(26,42)(27,41)(31,37)(32,36)(34,45)(43,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6015);