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×#1958 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
336 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 128 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)(21,23)(24,25,26,27)(28,29)(30,36)(31,39)(32,34)(33,37)(35,40)(38,42)(41,43);(25,27)(28,30,31,37,32,38,40,43)(29,33,35,36,34,41,39,42);(20,21,22,23)(29,34)(33,41)(35,39)(36,42)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7502, C19×#8528, C2×C19×#1958, … |
| maximal normal subgroup of | C19×#7502, C19×#8528, C2×C19×#1958, … |
| maximal quotient of | C19×#9639, C19×#9645, C19×#9681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 690);