Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88587 |
| automorphism | Aut(G) = C22×#1088⋊C2 (order 864) · Inn(G) = #1088⋊C2 · Out(G) = C22 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ SD16 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 26 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 26 points:
(1,3,13,11,5,12)(2,6,15)(4,10)(7,9,8,16,18,14)(19,20,22,24)(21,26,25,23);(1,2)(3,9)(4,7)(5,14)(6,10)(8,13)(11,18)(12,15)(16,17)(20,23)(21,25)(24,26)Polycyclic presentation:
2^4,3^3|b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^2,g^a=g^2,c^b=cd,e^b=f,f^b=e,g^b=g^2,e^c=e^2,f^c=f^2,f^e=fg23 conjugacy classes — view the full character table.
| maximal subgroup of | #11722294, #11722295, #11722296, … |
| maximal normal subgroup of | #11722294, #11722295, #11722296, … |
| maximal quotient of | #11720702, #11720703, #11720705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 234);