Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61106 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C29 |
| direct product | C13×#61107 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | C2×D42 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
2624 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)(16,25)(17,22)(18,34)(19,23)(20,28)(21,32)(24,35)(26,43)(27,42)(29,37)(30,38)(31,39)(33,40)(36,45)(41,44);(14,16,19,30)(15,20,23,37)(17,26,33,45)(18,29,35,28)(21,36,39,43)(22,41,40,42)(24,38,34,25)(27,32,44,31);(14,17)(15,21)(16,26)(18,31)(19,33)(20,36)(22,34)(23,39)(24,40)(25,41)(27,29)(28,44)(30,45)(32,35)(37,43)(38,42);(14,17)(15,22)(16,27)(18,32)(19,33)(20,36)(21,34)(23,40)(24,39)(25,42)(26,29)(28,45)(30,44)(31,35)(37,43)(38,41);(15,23)(20,37)(21,39)(22,40)(24,34)(25,38)(36,43)(41,42)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54095);