Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#22691 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator | C2×C4 | C23×C4×C13 |
| Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
846 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)(20,32)(21,36)(22,28)(23,30)(24,29)(25,31)(26,34)(27,33)(35,48)(37,45)(38,46)(39,44)(40,49)(41,43)(42,47);(18,20)(19,26)(21,22)(23,37)(24,34)(25,35)(27,43)(28,46)(29,48)(30,32)(31,45)(33,40)(36,49)(38,42)(39,41)(44,47);(18,21,23,38,25,39,24,33)(19,27,29,44,31,46,30,36)(20,22,37,42,35,41,34,40)(26,43,48,47,45,28,32,49);(18,22)(19,28)(20,33)(21,37)(23,42)(24,40)(25,41)(26,44)(27,32)(29,49)(30,47)(31,43)(34,39)(35,38)(36,45)(46,48)754 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 15679);