Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13307 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#13320 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| prime radical | C2×C13×#472 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C13×#131 ◁ G | |
540 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)(19,25)(20,30)(21,33)(22,23)(26,42)(27,34)(28,40)(29,41)(31,35)(32,38)(36,37)(39,44)(43,46)(45,48);(14,15)(16,17)(18,19,24,29)(20,26,32,45)(21,34,37,40)(22,28,23,27)(25,36,41,33)(30,46,38,44)(31,48,35,42)(39,47,43,49);(15,17)(18,20)(19,26)(21,35)(22,38)(23,30)(24,32)(25,39)(27,46)(28,44)(29,45)(31,37)(33,49)(34,42)(36,47)(40,48)(41,43)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 6308);