Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24398 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24403 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
1332 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,22,27,24,29,23,28)(20,25,31,40,33,42,32,41)(21,34,38,26,37,45,36,44)(30,46,35,39,48,43,47,49);(15,17)(18,20)(19,25)(21,35)(22,31)(23,32)(24,33)(26,43)(27,40)(28,41)(29,42)(30,36)(34,39)(37,47)(38,48)(44,46)(45,49);(18,21)(19,26)(20,30)(22,36)(23,38)(24,37)(25,39)(27,34)(28,45)(29,44)(31,47)(32,35)(33,48)(40,46)(41,43)(42,49);(15,17)(18,22,24,23)(19,27,29,28)(20,31,33,32)(21,36,37,38)(25,40,42,41)(26,34,44,45)(30,47,48,35)(39,46,49,43)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17391);