Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6196 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ C4⋊C4 |
107 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 17 points:
(2,8,6,4,5,9)(3,7)(10,12,13,11)(15,17);(1,2,4)(3,5,8,7,6,9)(10,11,13,12)(14,15)(16,17)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=c,b^a=bd,f^a=f^2,g^a=g^2,e^b=e^2,g^b=g^2,f^e=fg38 conjugacy classes — view the full character table.
| maximal subgroup of | #11720702, #11720703, #11720704, … |
| maximal normal subgroup of | #11720702, #11720703, #11720704, … |
| maximal quotient of | #11720304, #11720314, #11720315, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 96);