Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33×C4 · Schur multiplier (H2) = C2×C33 |
| direct product | C33×C4⋊C4 |
| unambiguous semidirect product | C4⋊(C33×C4) |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C33 | C22 |
| commutator | C2 | C2×C33×C4 |
| Frattini, cosocle | C22 | C22×C33 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C33 ◁ G | |
364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 3 generators on 17 points:
(1,2,3,4)(6,8)(9,10,11);(5,6,7,8)(12,13,14);(15,16,17)270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 514);