Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2883 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#2888 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | C22×C22⋊C4 |
| commutator | C22 | C23×C4×C19 |
| Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C2×C19×H(5,𝔽2) | C2 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C2×#41×C19 ◁ G | |
756 conjugacy classes of subgroups; only the 340 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,27,24,25,30,32)(22,26,29,33,28,31,34,35);(21,25)(23,30)(26,31)(29,34);(20,22)(21,26)(23,29)(24,28)(25,31)(27,33)(30,34)(32,35);(22,28)(26,31)(29,34)(33,35)779 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#13097, C19×#13099, C19×#21778, … |
| maximal normal subgroup of | C19×#13097, C19×#13099, C19×#21778, … |
| maximal quotient of | C19×#17350, C19×#17353, C19×#17367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1620);