Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C4 |
| direct product | C13×#7729 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C43×C13 ◁ G | |
346 conjugacy classes of subgroups.
| minimal degree | μ(G) = 61 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 61 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22,24,19)(17,25)(18,21)(20,26)(23,27,29,28)(30,31)(32,38,40,45)(33,37)(34,36)(35,39,43,41)(42,44)(46,47,49,53,50,52,58,60)(48,54,56,61,55,51,57,59);(14,16)(15,19)(17,23)(18,24)(20,27)(21,22)(25,28)(26,29)(30,32,34,40)(31,35,36,43)(33,41,42,39)(37,45,44,38)(46,48)(47,51)(49,57)(50,55)(52,54)(53,61)(56,58)(59,60);(14,17,18,26)(15,20,21,25)(16,23,24,29)(19,27,22,28)(31,36)(35,43)(37,44)(38,45)(47,52)(48,55)(53,60)(56,57)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 717);