Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2402 |
| 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 | |
400 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 216 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)(22,25)(23,24)(26,27)(28,29)(30,33)(31,35)(32,34)(36,37,39,41)(38,40,42,43);(21,24)(25,27)(28,30,32,31)(29,33,34,35)(36,38)(37,40)(39,42)(41,43);(28,31,32,30)(29,33,34,35)(38,42)(40,43);(20,22,23,26)(21,25,24,27)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10372, C19×#10373, C19×#21676, … |
| maximal normal subgroup of | C19×#10372, C19×#10373, C19×#21676, … |
| maximal quotient of | C19×#13846, C19×#13848, C19×#13854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1134);