Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #3273 |
520 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(10,18)(11,21)(13,23)(14,20)(16,22)(17,19);(5,7)(10,17)(13,22)(16,23)(18,19);(8,10)(9,13)(11,18)(12,17)(14,23)(15,22)(16,20)(19,21);(2,3)(4,5)(6,7)(8,9,12,15)(10,16,17,23)(11,20,21,14)(13,18,22,19)Polycyclic presentation:
2^7,3|a^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,h^a=h^2,c^b=cg,d^b=de,e^b=eg,e^d=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3273, C2×#83961, #11670359, … |
| maximal normal subgroup of | D3×#3273, C2×#83961, #11670359, … |
| maximal quotient of | #10786459, #10786540, #10786546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16537);