Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25140 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C25 |
| direct product | C13×#25145 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C2×#121 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C13×#3005 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ G | |
996 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)(18,19,24,37,23,28,22,27)(20,25,38,49,31,41,30,40)(21,32,34,26,36,43,35,44)(29,45,46,39,33,48,47,42);(15,17)(18,20,22,30,23,31,24,38)(19,25,27,40,28,41,37,49)(21,33,35,46,36,29,34,47)(26,42,32,48,44,39,43,45);(18,21)(19,26)(20,29)(22,34)(23,36)(24,35)(25,39)(27,43)(28,44)(30,46)(31,33)(32,37)(38,47)(40,48)(41,42)(45,49);(15,17)(18,22,23,24)(19,27,28,37)(20,30,31,38)(21,34,36,35)(25,40,41,49)(26,43,44,32)(29,46,33,47)(39,48,42,45)559 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 18133);