Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C3)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | H(3,𝔽3) ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | ((C3⋊D3)⋊C3)⋊C2 |
| commutator, hypocenter | H(3,𝔽3) | C42 |
| Frattini, socle | C22×C3 | D32 |
| Fitting, prime radical, cosocle | C22×H(3,𝔽3) | C22 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C22 | |
121 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)(14,15,16,17);(1,2,4)(3,5,8,7,6,9)(10,11,12,13)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=c,f^a=f^2,g^a=g^2,e^b=e^2,g^b=g^2,f^e=fg44 conjugacy classes — view the full character table.
| maximal subgroup of | #11720706, #11721076, #11721077, … |
| maximal normal subgroup of | #11720706, #11721076, #11721077, … |
| maximal quotient of | #11720302, #11720303, #11720310, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 94);