Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#2804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| prime radical | C22×D4×C19 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
480 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 192 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 — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(28,29,31,32)(30,33,34,35)(36,37)(38,41)(39,40)(42,43);(21,24)(25,27)(29,32)(30,34)(37,39)(38,42);(20,21)(22,25)(23,24)(26,27)(28,29)(30,33)(31,32)(34,35)(36,38,40,42)(37,41,39,43);(20,22,23,26)(21,25,24,27)(28,30)(29,33)(31,34)(32,35)(36,39,40,37)(38,43,42,41)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7745, C19×#7755, C19×#7782, … |
| maximal normal subgroup of | C19×#7745, C19×#7755, C19×#7782, … |
| maximal quotient of | C19×#14440, C19×#14457, C19×#14471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1536);