Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#3093 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C19×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
414 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 414 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) = 608 |
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)(31,34)(32,35)(36,39)(37,40)(38,41)(42,43);(21,24)(25,27)(28,30,32,38)(29,33,35,41)(31,37,39,43)(34,40,36,42);(20,22,23,26)(21,25,24,27)(29,34)(31,39)(33,40)(35,36)(37,43)(41,42);(29,35)(33,41)(34,36)(40,42)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#24020, C19×#24021, C19×#24022, … |
| maximal normal subgroup of | C19×#24020, C19×#24021, C19×#24022, … |
| maximal quotient of | C19×#20701, C19×#20845, C19×#20910, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1825);