Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#3255 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C23×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
342 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 176 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)(22,26)(28,29,33,36)(30,34,32,41)(31,38,40,42)(35,39,43,37);(20,21)(22,25)(23,24)(26,27)(28,30,33,32)(29,34,36,41)(31,39,40,37)(35,38,43,42);(21,24)(25,27)(28,31,33,40)(29,35,36,43)(30,37,32,39)(34,42,41,38);(20,22,23,26)(21,25,24,27)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10113, C19×#10115, C19×#10117, … |
| maximal normal subgroup of | C19×#10113, C19×#10115, C19×#10117, … |
| maximal quotient of | C19×#21894, C19×#21964, C19×#22118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1987);