Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#33409 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | C2×D8 |
| commutator | C8 | C23×C4×C13 |
| Frattini, cosocle | C2×C8 | C24×C13 |
| socle | C22×C13 | C22×D8 |
| prime radical | C24×C13 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
674 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)(20,29)(21,26)(22,36)(23,38)(24,28)(25,33)(27,30)(31,42)(32,43)(34,48)(35,41)(37,49)(39,46)(40,47)(44,45);(18,20,30,45,23,34,37,46,24,31,35,47,21,32,22,33)(19,25,36,43,26,40,41,42,28,39,49,48,38,44,27,29);(20,31)(25,39)(29,42)(32,34)(33,46)(40,44)(43,48)(45,47);(18,21,24,23)(19,26,28,38)(20,32,31,34)(22,35,37,30)(25,40,39,44)(27,36,41,49)(29,43,42,48)(33,47,46,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26397);