Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23912 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#24317 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
978 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,21)(16,20,17,19)(22,23,26,30)(24,32,34,28)(25,31,27,29)(33,37,35,36);(14,16,18,17)(15,19,21,20)(22,24)(23,28)(25,33)(26,34)(27,35)(29,37)(30,32)(31,36);(23,29)(25,27)(28,36)(30,31)(32,37)(33,35);(14,17,18,16)(15,20,21,19)(22,25,26,27)(23,29,30,31)(24,33,34,35)(28,37,32,36)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17305);