Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C26 |
| direct product | C13×#24293 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,26)(21,34)(22,37)(23,30)(24,29)(25,32)(27,38)(28,35)(31,46)(33,41)(36,40)(39,45)(42,47)(43,48)(44,49);(18,20,23,32,24,21,35,33)(19,25,28,26,29,41,30,34)(22,31,38,47,39,36,49,48)(27,40,37,42,44,46,45,43);(15,17)(18,21)(19,26)(20,24)(22,31)(23,33)(25,30)(27,43)(28,41)(29,34)(32,35)(36,39)(37,40)(38,47)(42,44)(45,46)(48,49);(18,22,35,49,24,39,23,38)(19,27,30,45,29,44,28,37)(20,31,33,48,21,36,32,47)(25,40,34,43,41,46,26,42)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 17281);