Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13316 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C13×#3054 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C22×C13×M16 ◁ G | |
552 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,28)(21,32)(22,37)(23,26)(24,29)(25,36)(27,35)(30,48)(31,45)(33,43)(34,44)(38,41)(39,47)(40,49)(42,46);(18,20,23,31)(19,24,26,39)(21,33,34,49)(22,38,35,30)(25,41,42,48)(27,43,37,40)(28,44,45,32)(29,46,47,36);(15,17)(21,34)(24,39)(25,42)(29,47)(32,44)(33,49)(36,46)(40,43)442 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6305);