Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2843 |
| 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 | |
348 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 348 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) = 2432 |
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)(20,21,23,25)(22,24,26,27)(28,29)(30,34)(31,35)(32,33);(22,26)(24,27)(29,33)(31,34)(36,37,39,41)(38,42,43,40);(20,21)(22,24)(23,25)(26,27)(28,30)(29,34)(31,33)(32,35)(36,38,39,43)(37,40,41,42);(20,22)(21,24)(23,26)(25,27)(28,31,32,34)(29,35,33,30)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12183, C19×#12259, C2×C19×#2843, … |
| maximal normal subgroup of | C19×#12183, C19×#12259, C2×C19×#2843, … |
| maximal quotient of | C19×#14638, C19×#14639, C19×#14640, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1575);