Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6229 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #41 |
220 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 3 generators on 17 points:
(2,5,6)(4,8,9)(11,15)(14,17);(1,2,4)(3,6,8)(5,9,7)(10,12,13,16)(11,14,15,17);(2,4)(5,9)(6,8)(10,11)(12,14)(13,15)(16,17)Polycyclic presentation:
2^4,3^3|b^2=d,c^a=cd,e^a=e^2,f^a=f^2,f^e=fg62 conjugacy classes — view the full character table.
| maximal subgroup of | #11720328, #11720522, #11720562, … |
| maximal normal subgroup of | #11720328, #11720522, #11720562, … |
| maximal quotient of | C4×#6229, #11721716, #11721718, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 387);