Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C33 · Schur multiplier (H2) = C2×C33 |
| direct product | C33×D8 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C33 | D4 |
| commutator, Frattini, cosocle | C4 | C22×C33 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C33 ◁ C33×C4 ◁ G | |
308 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3)(10,11,12,13,14,15,16,17);(4,5,6)(11,17)(12,16)(13,15);(7,8,9)189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 517);