Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of C9⋊SL(2,𝔽3) |
| automorphism | Aut(G) = C2×C3×D3×A4 (order 432) · Inn(G) = C3×A4 · Out(G) = C22×C3 |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C9×#41 ⋊ C3 |
| Sylow | #41 ⋊ 3−1+2 |
55 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,15)(2,9)(3,7)(4,14)(5,13)(6,12)(8,11)(10,16)(17,20,25,19,23,21,22,18,24);(3,4,9)(6,7,13)(10,12,11)(14,16,15)(18,20,23)(21,25,24)Polycyclic presentation:
2,3^3,2^3|a^2=g,c^3=d,e^2=g,f^2=g,c^b=cd,e^b=f,f^b=ef,f^e=fg62 conjugacy classes — view the full character table.
| maximal subgroup of | #11720752, #11721339, #11722411, … |
| maximal normal subgroup of | #11720752, #11721339, #11722411, … |
| maximal quotient of | C4×C9⋊SL(2,𝔽3), C2×#88683, (#41⋊C9)⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 330);