Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2081 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C22 |
| direct product | C19×#2082 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #397 |
| commutator, Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C23×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ G | |
184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,25,30,26,31,24,29)(22,32,35,27,36,43,34,44)(23,37,39,45,40,46,41,28)(33,48,49,51,38,42,50,47);(20,22,26,36)(21,27,31,44)(23,38,40,33)(24,35,25,34)(28,42,45,48)(29,43,30,32)(37,51,46,47)(39,49,41,50);(20,23,24,39,26,40,25,41)(21,28,29,37,31,45,30,46)(22,33,34,49,36,38,35,50)(27,42,32,47,44,48,43,51)437 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C19×#2082, C19×#23652, C19×#24987, … |
| maximal normal subgroup of | C2×C19×#2082, C19×#23652, C19×#24987, … |
| maximal quotient of | C19×#10632, C19×#10633, C19×#10635, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 814);