Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#2614 |
| 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 | |
782 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 232 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)(25,27)(28,29,32,35)(30,36,38,33)(31,34,40,39)(37,42,43,41);(21,23)(25,27)(28,30,32,38)(29,33,35,36)(31,37,40,43)(34,41,39,42);(20,21)(22,23)(24,25)(26,27)(28,29)(30,36)(31,39)(32,35)(33,38)(34,40)(37,41)(42,43);(28,31)(29,34)(30,37)(32,40)(33,41)(35,39)(36,42)(38,43)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#18225, C19×#18227, C19×#23905, … |
| maximal normal subgroup of | C19×#18225, C19×#18227, C19×#23905, … |
| maximal quotient of | C19×#14256, C19×#14263, C19×#14301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1346);