Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2859 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
472 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 264 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)(21,23)(26,29)(27,31)(32,33,37,36)(34,39,38,35);(24,25,28,30)(26,27,29,31)(32,34)(33,35)(36,39)(37,38);(20,21,22,23)(24,26,28,29)(25,27,30,31)(32,35,37,39)(33,38,36,34);(24,27)(25,29)(26,30)(28,31)(32,36,37,33)(34,39,38,35)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7660, C19×#7663, C19×#7680, … |
| maximal normal subgroup of | C19×#7660, C19×#7663, C19×#7680, … |
| maximal quotient of | C19×#14687, C19×#14699, C19×#14707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1591);