Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #1113 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
No aliases for this group.
| derived, Sylow | C33 ⋊ C42 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C22 | #1113 |
| commutator, hypocenter | C33 | C42 |
| Fitting, socle, prime radical, cosocle | C22×C33 | C22 |
| LCS | G ▷ C33 | |
| UCS | C1 ◁ C22 | |
178 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 17 points:
(1,2)(5,6)(7,8,9)(14,15,16,17);(2,3)(4,5,6)(8,9)(10,11,12,13)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=c,e^a=e^2,g^a=g^2,e^b=e^2,f^b=f^260 conjugacy classes — view the full character table.
| derived subgroup of | #88813⋊C3 |
| maximal subgroup of | #11722777, #11722795, D3×Dic32, … |
| maximal normal subgroup of | #11722777, #11722795, D3×Dic32, … |
| maximal quotient of | #11722070, #11722071, #11722082, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 460);