Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C13 · Schur multiplier (H2) = C23×C4 |
| direct product | C13×#10900 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C13 | #120 |
| commutator | C2×C4 | C2×C42×C13 |
| Frattini, cosocle | C23×C4 | C23×C13 |
| socle | C22×C13 | #386 |
| prime radical | C24×C13 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C13 ◁ C23×C4×C13 ◁ G | |
686 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,16)(18,19)(20,29)(21,34)(22,38)(23,27)(24,28)(25,31)(26,36)(30,45)(32,41)(33,40)(35,43)(37,42)(39,47)(44,46)(48,49);(18,20,23,31,24,33,22,32)(19,25,27,40,28,41,38,29)(21,30,36,46,37,47,35,48)(26,39,42,49,43,45,34,44);(14,16,17,15)(18,21)(19,26)(20,30)(22,35)(23,36)(24,37)(25,39)(27,42)(28,43)(29,44)(31,46)(32,48)(33,47)(34,38)(40,49)(41,45)832 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 3888);