Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32950 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32950 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3021 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1282 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,20)(16,24)(18,31)(22,33)(23,34)(25,41)(26,27)(28,29)(32,36)(35,44)(38,39)(40,42);(14,15,18,20,19,23,31,34)(16,21,26,32,27,37,24,36)(17,22,28,33,30,39,29,38)(25,35,41,43,42,44,40,45);(14,16)(15,21)(17,25)(18,26)(19,27)(20,32)(22,35)(23,37)(24,31)(28,41)(29,40)(30,42)(33,43)(34,36)(38,45)(39,44);(14,17)(15,22)(16,25)(18,28)(19,30)(20,33)(21,35)(23,39)(24,40)(26,41)(27,42)(29,31)(32,43)(34,38)(36,45)(37,44)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25938);