Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C19×#1786 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D4 |
| commutator | C2×C4 | C22×C4×C19 |
| Frattini, cosocle | C22×C4 | C23×C19 |
| prime radical | C23×D4×C19 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C23×C4×C19 ◁ G | |
848 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 848 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 608 |
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)(30,32)(31,34)(33,35);(29,32)(30,35)(33,34);(21,23)722 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#8375, C19×#8381, C19×#9017, … |
| maximal normal subgroup of | C19×#8375, C19×#8381, C19×#9017, … |
| maximal quotient of | C19×#8310, C19×#8313, C19×#8328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 518);