Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #99 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C22×C19×#101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22⋊C4 |
| commutator | C22 | C23×C4×C19 |
| Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C24×C19 | C2×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
736 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 360 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)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4);(5,6,8,12,9,11,17,19)(7,13,14,20,15,10,16,18);(5,7,9,15)(6,10,11,13)(8,16,17,14)(12,20,19,18)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10741, C19×#10750, C19×#10763, … |
| maximal normal subgroup of | C19×#10741, C19×#10750, C19×#10763, … |
| maximal quotient of | C22×C19×#324, C2×C19×#1461, C2×C19×#1463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1618);