Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#442 ⋊ C2 |
| Sylow | C3 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2)(9,13)(12,14);(2,3)(4,6,7,5);(9,12)(10,15)(13,14);(2,3)(4,5,7,6)(8,9)(10,12)(11,13)(14,15)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,e^2=g,b^a=be,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,h^c=h^2,h^d=h^266 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×AGL(1,ℤ/8), C2×#79865, C4×#5773, … |
| maximal normal subgroup of | C4×D3×AGL(1,ℤ/8), C2×#79865, C4×#5773, … |
| maximal quotient of | #10764604, #10764773, #10764789, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12441);