Finite Group DatabasebetaFinite Group Databasebeta| order | 432 |
| isoclinism | isoclinic class of #88390 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | (C22⋊C27)⋊C2 |
| commutator, cosocle, hypocenter | Q8⋊C27 | C2 |
| Frattini | C2×C9 | S4 |
| Fitting | Q8×C9 | D3 |
| socle, prime radical | C2×C3 | (C22⋊C9)⋊C2 |
| LCS | G ▷ Q8⋊C27 | |
| UCS | C1 ◁ C2 | |
29 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 432 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,6,10,13,5,15,12,7)(2,11,14,4,8,3,16,9)(18,21)(19,25)(20,28)(22,23)(24,34)(26,27)(29,36)(30,35)(31,41)(32,40)(33,39)(37,38)(42,43);(3,9,12)(4,10,11)(6,13,16)(7,14,15)(17,36,30,37,41,39,19,18,40,20,43,34,26,23,22,27,24,42,28,32,21,25,33,31,38,35,29)Polycyclic presentation:
2,3^3,2^3|a^2=g,b^3=c^2d,c^3=d^2,e^2=g,f^2=g,b^a=b^2c,c^a=c^2d,d^a=d^2,e^a=f,f^a=e,e^b=fg,f^b=ef,f^e=fg36 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#88390, #11720649, #11720650, … |
| maximal normal subgroup of | C2×#88390, #11720649, #11720650, … |
| maximal quotient of | #11720108, C2×#88390, #13046339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(432, 37);