Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24292 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26852 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#41 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
698 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 832 |
A minimal faithful permutation representation — 4 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,21)(17,19)(18,20)(22,23)(24,35)(25,41)(26,45)(27,33)(28,34)(29,38)(30,43)(31,36)(32,46)(37,49)(39,48)(40,50)(42,51)(44,52)(47,53);(14,16,18,17)(15,19,20,21)(22,24,27,38,28,40,46,39)(23,29,32,35,34,48,33,50)(25,42,43,53,44,26,37,36)(30,45,41,47,49,51,52,31);(14,17,18,16)(15,19,20,21)(22,25,27,43,28,44,46,37)(23,30,32,41,34,49,33,52)(24,36,38,42,40,53,39,26)(29,47,35,51,48,31,50,45);(15,20)(19,21)(22,26,27,36,28,42,46,53)(23,31,32,45,34,47,33,51)(24,37,38,25,40,43,39,44)(29,30,35,41,48,49,50,52)520 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19840);