Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#12996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator | C2×C8 | C22×C4×C13 |
| Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
512 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)(15,17)(18,19,21,27,22,28,37,42,24,30,38,41,23,29,35,25)(20,31,32,48,39,26,43,44,34,47,36,40,33,45,49,46);(14,15,16,17)(19,25)(21,35)(22,23)(26,40)(27,29)(28,41)(30,42)(31,46)(32,49)(33,39)(36,43)(37,38)(44,47)(45,48);(18,20)(19,26)(21,36)(22,39)(23,33)(24,34)(25,40)(27,46)(28,47)(29,31)(30,45)(32,38)(35,43)(37,49)(41,44)(42,48)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5984);