Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #2029⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2029⋊C3 |
| Fitting, Sylow | #2029 ⋊ C3 |
| derived | #543 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C22 | #120⋊C3 |
| commutator, cosocle, hypocenter | #543 | C2×C3 |
| Frattini | C24 | C2×A4 |
| Fitting | #2029 | C3 |
| LCS | G ▷ #543 | |
| UCS | C1 ◁ C22 | |
141 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 16 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,9,10,6,3,7)(8,16,15,14,12,11);(1,7,5,11)(2,12,8,3)(4,10,13,15)(6,16,14,9)Polycyclic presentation:
2,3,2^6|c^2=g,d^2=g,c^a=ce,d^a=dfh,c^b=d,d^b=cdh,e^b=fh,f^b=efh,d^c=dg,f^c=fh,e^d=eh30 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 609);