Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C13 · Schur multiplier (H2) = C24 |
| direct product | C13×#33647 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C13 |
| prime radical | C13×#3050 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C4×C13 ◁ C23×C8×C13 ◁ G | |
584 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)(16,19)(17,18)(20,21)(22,23)(24,28)(25,29)(26,39)(27,30)(31,36)(32,37)(33,40)(34,49)(35,41)(38,44)(42,46)(43,47)(45,50)(48,51)(52,53);(15,18)(19,21)(22,24,27,35)(23,28,30,41)(25,33,38,48)(26,34,37,47)(29,40,44,51)(31,42,45,52)(32,43,39,49)(36,46,50,53);(14,16,17,20)(15,19,18,21)(23,29)(25,36)(26,37)(28,40)(30,44)(31,32)(33,46)(34,47)(38,50)(39,45)(41,51)(42,43)(48,53)(49,52);(23,30)(28,41)(29,44)(31,45)(32,39)(40,51)(42,52)(43,49)598 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 26635);