Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32947 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#32947 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3027 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
1306 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)(18,29)(21,30)(22,31)(23,32)(24,36)(25,38)(27,39)(33,43)(34,41)(35,42)(40,44);(14,15,18,20,19,23,29,32)(16,21,25,30,26,34,38,41)(17,22,27,31,28,35,39,42)(24,33,37,40,36,44,45,43);(14,16)(15,21)(17,24)(18,25)(19,26)(20,30)(22,33)(23,34)(27,37)(28,36)(29,38)(31,40)(32,41)(35,44)(39,45)(42,43);(14,17)(15,22)(16,24)(18,27)(19,28)(20,31)(21,33)(23,35)(25,37)(26,36)(29,39)(30,40)(32,42)(34,44)(38,45)(41,43)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25935);