Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9263 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#9269 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #386 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C2×C42×C13 ◁ G | |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 37 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,19,18,21,16,20)(23,27)(24,31)(25,28)(30,35)(32,33)(34,36);(15,19)(16,17)(20,21)(22,23,28,35,26,30,25,27)(24,29,31,36,33,37,32,34);(15,19)(16,17)(20,21)(22,24)(23,29)(25,32)(26,33)(27,34)(28,31)(30,37)(35,36)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 2257);