Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6196 |
| automorphism | Aut(G) = C2×#11722315 (order 1728) · Inn(G) = ((C3⋊D3)⋊C3)⋊C2 · Out(G) = C2×D4 |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽3) ⋊ M16 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 72 |
A minimal faithful permutation representation — 2 generators on 17 points:
(2,8,6,4,5,9)(3,7)(10,12,13,15,14,16,17,11);(1,2,4)(3,5,8,7,6,9)(10,11,13,12,14,15,17,16)Polycyclic presentation:
2^4,3^3|a^2=c,b^2=c,c^2=d,b^a=bd,f^a=f^2,g^a=g^2,e^b=e^2,g^b=g^2,f^e=fg38 conjugacy classes — view the full character table.
| maximal subgroup of | #11720694, #11720697, #11720699, … |
| maximal normal subgroup of | #11720694, #11720697, #11720699, … |
| maximal quotient of | #11720303, #11720304, #11720323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 82);