Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2846 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2863 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C19 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C19 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ G | |
408 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 2432 |
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)(20,21,25,24)(22,27,23,26)(28,29,32,35)(30,33,34,31)(38,42)(40,43);(20,22,25,23)(21,26,24,27)(28,30,32,34)(29,33,35,31)(36,37,39,41)(38,40,42,43);(20,23,25,22)(21,27,24,26)(28,31,32,33)(29,34,35,30);(20,24,25,21)(22,27,23,26)(28,29)(30,33)(31,34)(32,35)(36,38)(37,40)(39,42)(41,43)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7669, C19×#7673, C19×#7689, … |
| maximal normal subgroup of | C19×#7669, C19×#7673, C19×#7689, … |
| maximal quotient of | C19×#14688, C19×#14699, C19×#14703, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1595);