Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#20710 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | #381 |
| commutator | C23 | C23×C4×C13 |
| Frattini, cosocle | C24 | C24×C13 |
| socle | C2×C13 | C2×#381 |
| prime radical | C22×C13×#41 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C23×C4×C13 ◁ G | |
1276 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)(18,22)(19,23)(21,30)(25,32,39,36)(26,37,40,33)(29,41)(31,35)(34,42)(38,43,45,44);(14,16)(15,20)(17,25)(18,26)(19,27)(21,32)(22,33)(23,24)(28,36)(29,38)(30,39)(31,40)(34,43)(35,37)(41,44)(42,45);(14,17)(15,21,23,28)(16,25)(18,29)(19,30)(20,32,24,36)(22,34,35,41)(26,38)(27,39)(31,42)(33,43,37,44)(40,45);(14,18,19,31)(15,22,23,35)(16,26,27,40)(17,29,30,42)(20,33,24,37)(21,34,28,41)(25,38,39,45)(32,43,36,44)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 13698);