Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of AGL(1,ℤ/8) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C2×C19×#442 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D4 |
| commutator | C4 | C23×C4×C19 |
| Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | C22×D8×C19 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ G | |
608 conjugacy classes of subgroups; only the 296 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 296 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(3,4,6,5)(7,8,10,12)(9,11,14,13);(8,11)(9,14)(12,13);(3,5,6,4)(8,12)(11,13)836 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#9089, C19×#9093, C19×#12647, … |
| maximal normal subgroup of | C19×#9089, C19×#9093, C19×#12647, … |
| maximal quotient of | C2×C19×#1580, C2×C19×#1586, C2×C19×#1594, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1674);