Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of Dic54 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C27 ⋊ C2 |
| Sylow | C27 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D27 |
| commutator | C2×C27 | C2×C4 |
| Frattini | C4×C9 | C2×D3 |
| Fitting | C8×C27 | C2 |
| socle | C2×C3 | C4×D9 |
| prime radical | C2×D27 | C4 |
| cosocle | C4×C27 | C22 |
| hypercenter | C8 | D27 |
| hypocenter | C27 | M16 |
| LCS | G ▷ C2×C27 ▷ C27 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 216 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,25,24,10,8,5,22,20,23,4,7,26,9,19,14,3,27,6,12,17,13,21,2,18,11,16,15)(28,29,30,33,31,32,34,35);(2,5)(3,9)(4,12)(6,7)(8,18)(10,11)(13,20)(14,19)(15,25)(16,24)(17,23)(21,22)(26,27)(29,32)(33,35)Polycyclic presentation:
2^4,3^3|b^2=c,c^2=d,e^3=f^2g,f^3=g^2,b^a=bd,e^a=e^2f,f^a=f^2g,g^a=g^2114 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#88359, #11720151, M16×D27, … |
| maximal normal subgroup of | C2×#88359, #11720151, M16×D27, … |
| maximal quotient of | Dic27⋊C8, #11720056, (C2×D27)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 6);