Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13469 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C22 |
| direct product | C13×#13469 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2065 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
306 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)(14,15,22,26,21,27,20,40)(16,28,17,32,31,41,36,43)(18,37,39,45,19,38,33,25)(23,35,44,29,42,34,24,30);(14,16,18,29,20,17,33,34,21,31,19,30,22,36,39,35)(15,23,25,28,26,24,37,43,27,42,45,41,40,44,38,32);(14,17)(15,24)(16,20)(18,30)(19,29)(21,36)(22,31)(23,26)(25,41)(27,44)(28,45)(32,38)(33,34)(35,39)(37,43)(40,42)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6457);