Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12997 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#41 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
492 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(15,17)(18,19,23,30,22,29,38,26,25,32,21,28,24,31,39,42)(20,33,36,41,40,27,43,45,37,47,34,48,35,46,49,44);(14,15,16,17)(19,26)(21,38)(22,24)(23,39)(27,41)(28,31)(29,30)(32,42)(33,45)(34,43)(35,40)(36,49)(44,47)(46,48);(18,20)(19,27)(21,36)(22,40)(23,34)(24,35)(25,37)(26,41)(28,45)(29,47)(30,44)(31,33)(32,46)(38,49)(39,43)(42,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5985);