Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #3754⋊C3 |
| automorphism | Aut(G) = C2×D4×((C3⋊D3)⋊C3)⋊C2 (order 1728) · Inn(G) = #638⋊C3 · Out(G) = C23 |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | #3753⋊C3 |
| Fitting | D4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ D8 |
93 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(2,5)(3,8)(6,7)(9,10,16)(11,13,15)(12,14,17);(1,2)(3,5)(4,7)(6,8)(10,12)(11,14)(13,15)(16,17)Polycyclic presentation:
2^2,3,2^2,3^2|d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,d^b=de,f^c=fg41 conjugacy classes — view the full character table.
| maximal subgroup of | #11721190, #11721191, #11721192, … |
| maximal normal subgroup of | #11721190, #11721191, #11721192, … |
| maximal quotient of | #63634⋊C3, #63636⋊C3, #63653⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 153);