Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26850 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#2002 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
776 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,21)(17,19)(18,20)(22,23)(24,26)(25,27)(28,32)(29,33)(30,34)(31,37)(35,36);(14,16,18,17)(15,19,20,21)(22,24,28,31,29,35,27,34)(23,30,25,36,33,37,32,26);(14,17,18,16)(15,19,20,21)(22,25,27,23,29,32,28,33)(24,30,34,26,35,37,31,36);(15,20)(19,21)(22,26,28,30,29,36,27,37)(23,31,25,35,33,34,32,24)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19838);