Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#1344 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #99 |
| commutator | C22×C4 | C2×C4×C19 |
| Frattini, cosocle | C2×C22⋊C4 | C22×C19 |
| prime radical | C24×C19 | D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C19 ◁ C2×C22⋊C4×C19 ◁ G | |
146 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 608 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,24)(23,26)(25,27)(28,29)(30,36)(31,39,40,34)(32,35)(33,37,41,43)(38,42);(21,24)(22,27)(25,26)(28,30,32,38)(29,33,35,41)(31,37,40,43)(34,36,39,42)437 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#1344, C19×#11691, C19×#11692, … |
| maximal normal subgroup of | C2×C19×#1344, C19×#11691, C19×#11692, … |
| maximal quotient of | C19×#7077, C19×#7079, C19×#7085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 76);