Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13023 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
474 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)(18,19,23,29,38,47,22,26,25,31,21,28,24,30,39,43)(20,32,35,27,41,42,40,49,37,48,33,46,36,44,34,45);(14,15,16,17)(19,26)(21,22)(23,39)(24,38)(27,42)(28,30)(29,47)(31,43)(32,49)(33,40)(34,35)(36,41)(44,46)(45,48);(18,20)(19,27)(21,34)(22,35)(23,40)(24,41)(25,37)(26,42)(28,32)(29,48)(30,49)(31,46)(33,39)(36,38)(43,44)(45,47)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6011);