Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1913 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#1913 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #386 |
| commutator | C23 | C22×C4×C19 |
| Frattini, cosocle | C24 | C23×C19 |
| prime radical | C19×#534 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C24×C19 ◁ G | |
380 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 3 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,25,29,33)(23,30,31,26)(24,27)(28,32)(34,35);(20,22)(21,25,27,33)(23,28)(24,29)(26,32,30,35)(31,34);(20,23)(21,26)(22,28)(24,31)(25,32)(27,30)(29,34)(33,35)551 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12753, C19×#12754, C19×#12767, … |
| maximal normal subgroup of | C19×#12753, C19×#12754, C19×#12767, … |
| maximal quotient of | C19×#9107, C19×#9108, C19×#9109, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 645);