Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2644 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
420 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(25,26)(28,29)(30,33)(31,34)(32,35)(36,37,40,42)(38,43,39,41);(20,21,23,24)(22,25,27,26)(28,30)(29,31)(32,34)(33,35)(36,38,40,39)(37,41,42,43);(20,21)(22,26)(23,24)(25,27)(28,30)(29,33)(31,35)(32,34)(36,37)(38,41)(39,43)(40,42);(20,22,23,27)(21,25,24,26)(28,31,32,33)(29,34,35,30)(36,39,40,38)(37,41,42,43)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#29436, C19×#29437, C19×#29442, … |
| maximal normal subgroup of | C19×#29436, C19×#29437, C19×#29442, … |
| maximal quotient of | C19×#14260, C19×#14266, C19×#14331, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1376);