Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2634 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
416 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(25,28)(29,31)(32,33,37,35)(34,40,42,38)(36,39,44,43)(41,46,47,45);(21,23)(25,28)(29,31)(32,34,37,42)(33,38,35,40)(36,41,44,47)(39,45,43,46);(20,21)(22,23)(24,25)(26,29)(27,28)(30,31)(32,35,37,33)(34,38,42,40)(36,39,44,43)(41,46,47,45);(24,26,27,30)(25,29,28,31)(32,36)(33,39)(34,41)(35,43)(37,44)(38,45)(40,46)(42,47)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#9190, C19×#10021, C19×#10025, … |
| maximal normal subgroup of | C19×#9190, C19×#10021, C19×#10025, … |
| maximal quotient of | C19×#14270, C19×#14289, C19×#14298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1366);