Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88436 |
| automorphism | Aut(G) = C2×D4×((C3⋊D3)⋊C3)⋊C2 (order 1728) · Inn(G) = #6200 · Out(G) = C23 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ Q16 |
75 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(2,8,6,4,5,9)(3,7)(10,12,19,23,14,21,13,20)(11,15,22,25,17,24,16,18);(1,2,4)(3,5,8,7,6,9)(10,11,14,17)(12,18,21,25)(13,22,19,16)(15,23,24,20)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=cd,c^2=d,b^a=bc,c^a=cd,f^a=f^2,g^a=g^2,e^b=e^2,g^b=g^2,f^e=fg29 conjugacy classes — view the full character table.
| maximal subgroup of | #11720851, #11720852, #11720853, … |
| maximal normal subgroup of | #11720851, #11720852, #11720853, … |
| maximal quotient of | #11720306, #11720309, #11720326, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 86);