Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9183 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#9197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#2619 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
624 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 416 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,19,17,20,21,18)(22,23)(24,30)(25,33,35,28)(26,32)(27,29)(31,34,37,36);(15,18)(16,21)(19,20)(22,24,30,23,27,32,26,29)(25,31,34,28,35,37,36,33);(22,25)(23,28)(24,31)(26,36)(27,35)(29,33)(30,34)(32,37)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2185);