Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2399 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C23 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| socle, prime radical | C23×C19 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
504 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(24,25,28,31)(26,30,27,29)(32,33,36,39)(34,38,35,37);(20,21)(22,23)(24,26,28,27)(25,29,31,30)(32,34,36,35)(33,37,39,38);(21,23)(24,26,28,27)(25,30,31,29)(32,35,36,34)(33,38,39,37);(24,27,28,26)(25,29,31,30)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#9030, C19×#10014, C19×#10017, … |
| maximal normal subgroup of | C19×#9030, C19×#10014, C19×#10017, … |
| maximal quotient of | C19×#13848, C19×#13850, C19×#13856, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1131);