Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C23 |
| direct product | C13×#13412 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C13×#405 ◁ G | |
430 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)(15,16)(18,19)(20,25)(21,26)(22,39)(23,40)(24,29)(27,36)(28,37)(30,48)(31,44)(32,49)(33,42)(34,46)(35,43)(38,47)(41,45);(14,15)(16,17)(18,20,24,34)(19,25,29,46)(21,35,38,32)(22,30,36,31)(23,41,37,33)(26,43,47,49)(27,44,39,48)(28,42,40,45);(14,16,17,15)(19,26)(20,30)(21,36)(22,38)(23,37)(25,42)(27,28)(29,47)(31,34)(32,41)(33,35)(39,40)(44,48)(45,46)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6400);