Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #3746⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #3746⋊C3 |
| Sylow | H(3,𝔽3) ⋊ Q16 |
71 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 144 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,3,10,14,5,12,4,11)(2,6,13,16,8,15,7,9)(17,18,24)(19,21,23)(20,22,25);(1,2,5,8)(3,9,12,16)(4,13,10,7)(6,14,15,11)(18,20)(19,22)(21,23)(24,25)Polycyclic presentation:
2^2,3,2^2,3^2|a^2=e,b^2=de,d^2=e,b^a=bd,d^a=de,f^a=f^2,g^a=g^2,f^c=fg53 conjugacy classes — view the full character table.
| maximal subgroup of | #11720249, #11720250, #11720254, … |
| maximal normal subgroup of | #11720249, #11720250, #11720254, … |
| maximal quotient of | #63643⋊C3, #63645⋊C3, C2×#3746⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 114);