Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32700 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#32701 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2760 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C13×#534 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C24×C13 ◁ G | |
628 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)(14,15)(16,24,27,20)(17,28,31,21)(18,22)(19,23)(25,38)(26,34,40,36)(29,33)(30,41,43,35)(32,37)(39,44)(42,45);(14,16)(15,20)(17,29)(18,26)(19,27)(21,33)(22,36)(23,24)(25,31)(28,38)(30,42)(32,40)(34,37)(35,45)(39,43)(41,44);(14,17)(15,21)(16,25,27,29)(18,30)(19,31)(20,33,24,38)(22,35)(23,28)(26,39,40,42)(32,43)(34,44,36,45)(37,41);(14,18,19,32)(15,22,23,37)(16,26,27,40)(17,30,31,43)(20,34,24,36)(21,35,28,41)(25,39,29,42)(33,44,38,45)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25689);