Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C2×C42 |
No aliases for this group.
| Fitting, derived, Sylow | #2811 ⋊ C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #5464 |
| commutator, Fitting, cosocle, hypocenter | #2811 | C3 |
| Frattini, socle | C23 | C22⋊A4 |
| LCS | G ▷ #2811 | |
| UCS | C1 ◁ C2 | |
107 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,6)(3,7,17)(4,13,18)(5,10,16)(8,20,12)(9,22,15)(11,21,23)(14,19,24);(1,15,5,4)(2,9,10,13)(3,14,12,11)(6,16)(7,19,8,21)(17,20)(18,22)(23,24);(1,12,5,3)(4,11,15,14)(6,17,16,20)(18,24,22,23)Polycyclic presentation:
3,2^7|b^2=g,c^2=f,d^2=f,e^2=fg,b^a=cg,c^a=bc,d^a=ef,e^a=de,f^a=fg,g^a=f,h^a=fh,d^b=dh,e^b=egh,d^c=df,e^c=efh16 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5866);