Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C2 |
| direct product | C19×#1676 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C19 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
144 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,24,27)(22,28,31,35)(23,32,29,26)(25,33,34,30)(36,37,40,43)(38,44,46,51)(39,47,49,42)(41,48,50,45);(20,22,29,33,24,31,23,30)(21,25,32,35,27,34,26,28);(36,38,40,46)(37,41,43,50)(39,48,49,45)(42,51,47,44)551 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12384, C19×#12385, C19×#12386, … |
| maximal normal subgroup of | C19×#12384, C19×#12385, C19×#12386, … |
| maximal quotient of | C19×#8645, C19×#9216, C19×#9568, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 408);