Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#1674 |
| 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 | |
156 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 156 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) = 43 |
| transitive degree | μt(G) = 2432 |
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)(22,25)(26,27)(28,29,32,35)(30,36,38,43)(31,39,41,34)(33,40,42,37);(20,21,25,27,23,26,22,24);(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36)551 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12380, C19×#12381, C19×#12382, … |
| maximal normal subgroup of | C19×#12380, C19×#12381, C19×#12382, … |
| maximal quotient of | C19×#8645, C19×#9218, C19×#9566, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 406);