Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6229 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#1084 |
| Sylow | H(3,𝔽3) ⋊ C4⋊C4 |
143 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 3 generators on 17 points:
(2,5,6)(4,8,9)(14,15,16,17);(2,4)(5,9)(6,8)(10,11,12,13)(15,17);(1,2,4)(3,6,8)(5,9,7)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=f^2,f^e=fg62 conjugacy classes — view the full character table.
| maximal subgroup of | #11720306, #11720307, #11720308, … |
| maximal normal subgroup of | #11720306, #11720307, #11720308, … |
| maximal quotient of | C4⋊#6180, #11720550, #11720551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 188);