Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #32894 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#32896 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C13 | #2846 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×H(7,𝔽2) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C13 ◁ C22×C4×C13 ◁ G | |
3610 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)(14,15,20,26)(16,27,30,40)(17,23,32,39)(18,25,19,24)(21,33,37,29)(22,34,38,31)(28,35,45,42)(36,44,41,43);(14,16)(15,21)(17,28)(18,33)(19,29)(20,30)(22,35)(23,36)(24,40)(25,27)(26,37)(31,44)(32,45)(34,43)(38,42)(39,41);(14,17)(15,22)(16,28)(18,31)(19,34)(20,32)(21,35)(23,24)(25,39)(26,38)(27,41)(29,43)(30,45)(33,44)(36,40)(37,42);(14,17)(15,23)(16,28)(18,34)(19,31)(20,32)(21,36)(22,24)(25,38)(26,39)(27,42)(29,44)(30,45)(33,43)(35,40)(37,41)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 25884);