Finite Group DatabasebetaFinite Group Databasebeta| order | 2432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D4×D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | D4×SD16×C19 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C19 |
| prime radical | D42×C19 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 608 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4)(13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31);(2,4);(5,6,7,8,9,10,11,12);(6,8)(7,11)(10,12)665 conjugacy classes — view the full character table.
| maximal subgroup of | C19×#19756, C19×#19757, C19×#19763, … |
| maximal normal subgroup of | C19×#19756, C19×#19757, C19×#19763, … |
| maximal quotient of | C19×#19763, C19×#19764, C19×#19765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2432, 2013);