Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10144 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10148 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#3151 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
614 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,19)(16,17)(20,21)(22,23)(24,32)(25,28)(26,30)(27,31)(29,34)(33,37)(35,36);(14,15,18,21)(16,20,17,19)(23,28)(24,33)(25,26)(30,31)(32,36)(34,35);(15,19)(16,17)(20,21)(22,24)(23,29)(25,33)(26,34)(27,35)(28,32)(30,36)(31,37)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3136);