Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C42 |
| direct product | C19×#2641 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C2×C19×#127 | C2 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
584 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25)(26,29)(27,28)(30,31)(33,36)(37,38);(20,21,22,23)(25,28)(29,30)(32,33,35,36)(34,37,39,38);(20,21)(22,23)(24,25)(26,30)(27,28)(29,31)(32,33)(34,38)(35,36)(37,39);(24,26,27,31)(25,29,28,30)(32,34,35,39)(33,37,36,38)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10089, C19×#10097, C19×#18430, … |
| maximal normal subgroup of | C19×#10089, C19×#10097, C19×#18430, … |
| maximal quotient of | C19×#14260, C19×#14272, C19×#14283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1373);