Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61100 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| socle | C2×C13 | C2×D42 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ G | |
2616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,26)(17,28)(18,22)(19,23)(20,24)(21,25)(27,42)(29,31)(30,43)(32,36)(33,45)(34,39)(35,41)(37,40)(38,44);(14,16)(15,17)(18,33)(19,28)(20,36)(21,29)(22,38)(23,31)(24,26)(25,32)(27,34)(30,40)(35,43)(37,44)(39,45)(41,42);(14,17)(15,16)(18,30)(19,31)(20,26)(21,32)(22,27)(23,28)(24,36)(25,29)(33,40)(34,38)(35,45)(37,42)(39,43)(41,44);(14,18)(15,22)(16,27)(17,30)(19,34)(20,37)(21,35)(23,39)(24,40)(25,41)(26,42)(28,43)(29,44)(31,38)(32,45)(33,36);(14,19,21,20)(15,23,25,24)(16,28,29,36)(17,31,32,26)(18,34,35,37)(22,39,41,40)(27,43,44,33)(30,38,45,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54088);