Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10260 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#10279 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C13 | #121 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 3328 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,24,21)(20,28,32,29)(22,27,23,26)(25,31,33,30)(34,35,38,41)(36,42,44,49)(37,45,47,40)(39,46,48,43);(15,17)(18,20,24,32)(19,25,21,33)(22,31,23,30)(26,29,27,28);(18,21,24,19)(20,29,32,28)(22,26,23,27)(25,30,33,31)(34,36,38,44)(35,39,41,48)(37,46,47,43)(40,49,45,42)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3267);