Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2212 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#12820 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #459 |
| 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 ◁ C2×C4×C8×C13 ◁ G | |
414 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)(14,15,16,17)(18,19)(20,28)(21,33)(22,37)(23,39)(24,29)(25,31)(26,30)(27,38)(32,46)(34,45)(35,49)(36,41)(40,42)(43,47)(44,48);(18,20,22,31,24,32,38,23)(19,25,27,28,29,39,37,46)(21,30,34,47,36,48,35,40)(26,41,42,45,44,33,43,49);(18,21)(19,26)(20,30)(22,34)(23,40)(24,36)(25,41)(27,42)(28,45)(29,44)(31,47)(32,48)(33,39)(35,38)(37,43)(46,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 5808);