Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #6308 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Sylow | C33 ⋊ C4⋊C4 |
364 conjugacy classes of subgroups.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2,3,4)(6,8)(15,16,17);(5,6,7,8)(10,11)(13,14)(16,17);(12,13,14);(9,10,11)Polycyclic presentation:
2^4,3^3|a^2=d,b^2=c,b^a=bd,e^a=e^2,f^a=f^2,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | #11723389, #11723390, #11723393, … |
| maximal normal subgroup of | #11723389, #11723390, #11723393, … |
| maximal quotient of | #11722177, #11722178, #11722184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 504);