Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#1634 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C19×#555 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
218 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 68 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 — 3 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)(22,26)(25,27)(28,29,33,36)(30,37,39,42)(31,35,32,40)(34,41,43,38);(22,26)(24,27)(28,30,33,39)(29,34,36,43)(31,38,32,41)(35,42,40,37);(20,21,23,25)(22,27,26,24)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7521, C19×#13682, C2×C19×#1634, … |
| maximal normal subgroup of | C19×#7521, C19×#13682, C2×C19×#1634, … |
| maximal quotient of | C19×#7758, C19×#7760, C19×#7785, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 366);