Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#1850 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C23 |
| commutator | C22 | C22×C8×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| socle | C23×C19 | C22×C4 |
| prime radical | C24×C19 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
348 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 160 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)(20,21)(22,23)(24,25)(26,27)(28,29,32,30,31,33,35,34);(21,23)(28,30,32,33,31,34,35,29);(25,27)1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#7064, C19×#8851, C19×#8852, … |
| maximal normal subgroup of | C19×#7064, C19×#8851, C19×#8852, … |
| maximal quotient of | C19×#8829, C19×#8830, C19×#8831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 582);