Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#26271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C13 |
| prime radical | C2×C13×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ G | |
752 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)(16,20)(17,18)(19,21)(22,23)(24,35)(25,41)(26,44)(27,33)(28,34)(29,38)(30,37)(31,46)(32,45)(36,51)(39,49)(40,52)(42,48)(43,53)(47,50);(15,18)(19,20)(22,24,27,38,28,40,45,39)(23,29,32,35,34,49,33,52)(25,26,37,46,43,47,42,36)(30,50,41,31,48,44,53,51);(22,25,27,37,28,43,45,42)(23,30,32,41,34,48,33,53)(24,36,38,26,40,46,39,47)(29,31,35,44,49,51,52,50);(14,16,17,21)(15,19,18,20)(22,26,45,36,28,47,27,46)(23,31,33,50,34,51,32,44)(24,37,39,25,40,42,38,43)(29,48,52,41,49,30,35,53)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 19259);