Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#1974 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| socle | C22×C19 | C4×D4 |
| prime radical | C2×C19×#135 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C8×C19 ◁ G | |
300 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 608 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,32,29,33,27,30)(26,34,36,39,37,38,35,31);(20,21,22,23)(25,30,33,32)(31,38,39,34);(24,26,27,35,29,37,28,36)(25,31,32,34,33,39,30,38)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7114, C19×#13011, C19×#13027, … |
| maximal normal subgroup of | C19×#7114, C19×#13011, C19×#13027, … |
| maximal quotient of | C19×#9655, C19×#9656, C19×#9657, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 706);