Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#2132 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C19 | #99 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×Q8 | C23×C19 |
| socle | C2×C19 | C2×#99 |
| prime radical | C19×#532 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C19 ◁ C2×C4×C19 ◁ C2×#41×C19 ◁ G | |
250 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 250 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) = 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)(20,21,24,29,25,30,22,27)(23,28,31,35,32,26,33,34);(21,26)(23,32)(27,34)(28,30)(29,35)(31,33);(20,22,25,24)(21,27,30,29)(23,31,32,33)(26,34,28,35)494 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#7484, C19×#7488, C19×#7492, … |
| maximal normal subgroup of | C19×#7484, C19×#7488, C19×#7492, … |
| maximal quotient of | C19×#11431, C19×#11447, C19×#11475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 864);