Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19883 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#19894 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C13 |
| prime radical | C13×#547 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C42×C13 ◁ G | |
640 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,20)(16,18,21,19)(23,27)(25,34)(28,35)(29,30)(31,36)(32,37);(22,23,26,30)(24,31,33,28)(25,29,34,27)(32,35,37,36);(15,18)(16,21)(19,20)(22,24,26,33)(23,28,30,31)(25,32,34,37)(27,35,29,36);(23,29)(25,34)(27,30)(28,36)(31,35)(32,37)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 12882);