Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2613 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#2642 |
| 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 | |
416 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 200 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(26,30)(28,31)(33,37)(38,40)(39,45)(46,47);(20,21,22,23)(24,25,27,29)(26,28,30,31)(32,33)(34,40)(35,39)(36,37)(38,42)(41,47)(43,46)(44,45);(20,21)(22,23)(24,26)(25,28)(27,30)(29,31)(32,34,36,42)(33,38,37,40)(35,43,44,41)(39,47,45,46);(32,35,36,44)(33,39,37,45)(34,41,42,43)(38,46,40,47)608 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#10095, C19×#10103, C19×#18441, … |
| maximal normal subgroup of | C19×#10095, C19×#10103, C19×#18441, … |
| maximal quotient of | C19×#14261, C19×#14274, C19×#14283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1374);