Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#1728 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C23 |
| commutator | C22 | C2×C42×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 | |
480 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 248 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)(28,29,30,33,31,32,34,35);(21,23)(24,25,26,27);(29,32)(33,35)1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#7026, C19×#7034, C19×#7037, … |
| maximal normal subgroup of | C19×#7026, C19×#7034, C19×#7037, … |
| maximal quotient of | C19×#7848, C19×#7850, C19×#7852, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 460);