Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1685 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C4 |
| direct product | C19×#1688 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C19 |
| prime radical | C19×#493 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C42×C19 ◁ G | |
184 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 1216 |
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)(21,24)(22,25)(26,27)(29,32)(30,34)(33,35);(20,21,25,27,23,26,22,24);(21,26)(24,27)(28,29,31,33)(30,35,34,32)437 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12336, C19×#12337, C19×#12360, … |
| maximal normal subgroup of | C19×#12336, C19×#12337, C19×#12360, … |
| maximal quotient of | C19×#8653, C19×#9230, C19×#9572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 420);