Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#2044 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #120 |
| commutator, Frattini, cosocle | C24 | C23×C19 |
| prime radical | C19×#534 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ G | |
382 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,22)(24,25)(26,28)(27,29)(30,31);(20,21)(22,23)(24,26)(25,28)(27,30)(29,31);(20,22,23,21)(28,31)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#12132, C19×#12133, C19×#12134, … |
| maximal normal subgroup of | C19×#12132, C19×#12133, C19×#12134, … |
| maximal quotient of | C19×#10394, C19×#10395, C19×#10396, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 776);