Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C26 |
| direct product | C2×C19×#407 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C19 | C23 |
| commutator | C22 | C23×C4×C19 |
| Frattini, cosocle | C2×C4 | C24×C19 |
| socle | C23×C19 | C22×C4 |
| prime radical | C25×C19 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C19 ◁ G | |
1008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 608 |
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)(5,6)(7,8,9,12,10,11,13,14);(4,6);(8,11)(12,14)1064 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C19×#7909, C19×#7911, C19×#7913, … |
| maximal normal subgroup of | C19×#7909, C19×#7911, C19×#7913, … |
| maximal quotient of | C2×C19×#1462, C2×C19×#1463, C2×C19×#1464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 1609);