Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#1488 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C42 | C23×C19 |
| socle | C22×C19 | C2×C22⋊C4 |
| prime radical | C2×#41×C19 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ G | |
246 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,25,23,24,26,27)(28,29)(30,37)(31,35)(32,40)(33,36)(34,38)(39,42)(41,43);(28,30)(29,34)(31,38)(32,41)(33,39)(35,42)(36,43)(37,40);(21,24)(25,27)(28,31,33,32)(29,35,36,40)(30,38,39,41)(34,42,43,37)722 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#8412, C19×#8413, C19×#8414, … |
| maximal normal subgroup of | C19×#8412, C19×#8413, C19×#8414, … |
| maximal quotient of | C19×#7608, C19×#7611, C19×#7612, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 220);