Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C4×H(3,𝔽3) ⋊ C22 |
| Sylow | H(3,𝔽3) ⋊ C2×D4 |
205 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 36 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2,9)(3,6,4)(5,8,7)(10,11,12,13);(2,4)(3,7)(5,8)(6,9)(11,13);(3,7)(5,6)(8,9)(11,13)Polycyclic presentation:
2^4,3^3|c^2=d,c^a=cd,f^a=f^2,g^a=g^2,c^b=cd,e^b=e^2,g^b=g^2,f^e=fg32 conjugacy classes — view the full character table.
| maximal subgroup of | #11720695, #11720699, #11720837, … |
| maximal normal subgroup of | #11720695, #11720699, #11720837, … |
| maximal quotient of | #11720833, #11720837, #11720838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 302);