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×#2834 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C24×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
372 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 168 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)(25,27)(28,29)(30,32)(31,33)(34,35)(36,37,40,42)(38,39,41,43);(22,26)(25,27)(28,29,31,33)(30,34,35,32)(36,38)(37,39)(40,41)(42,43);(20,21,23,24)(22,25,26,27)(28,29)(30,34)(31,33)(32,35)(36,39)(37,41)(38,42)(40,43);(20,22)(21,25)(23,26)(24,27)(28,30)(29,32)(31,35)(33,34)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12138, C19×#12232, C2×C19×#2834, … |
| maximal normal subgroup of | C19×#12138, C19×#12232, C2×C19×#2834, … |
| maximal quotient of | C19×#14627, C19×#14636, C19×#14644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1566);