Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of C3⋊PSU(3,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C3 |
No aliases for this group.
| Sylow | C33 ⋊ C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C3⋊PSU(3,𝔽2) |
| commutator | C3×C3⋊D3 | C2×C4 |
| Fitting, socle | C2×C33 | Q8 |
| prime radical, cosocle | C2×C3×C3⋊D3 | C22 |
| hypocenter | C33 | C4⋊C4 |
| LCS | G ▷ C3×C3⋊D3 ▷ C33 | |
| UCS | C1 ◁ C2 | |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,3)(4,10,9,11)(6,7,12,8);(2,3)(5,7,9,11)(6,10,8,12)(13,14,15,16)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=cd,b^a=bcd,e^a=e^2f,f^a=ef,g^a=g^2,e^b=f^2,f^b=e,e^c=e^2,f^c=f^224 conjugacy classes — view the full character table.
| maximal subgroup of | GO+(4,𝔽2)⋊Dic3, #11724100, #11724104, … |
| maximal normal subgroup of | GO+(4,𝔽2)⋊Dic3, #11724100, #11724104, … |
| maximal quotient of | #11722804, #11722806, #11722808, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 593);