Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#100 ⋊ C2 |
| Sylow | C3 ⋊ #2037 |
326 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2)(4,6,7,5)(9,12)(10,15)(13,14);(4,5)(6,7)(10,15)(12,13);(2,3)(5,6)(8,9)(10,12)(11,14)(13,15)Polycyclic presentation:
2^7,3|c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,e^c=eg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2037, C2×#70066, #10822784, … |
| maximal normal subgroup of | D3×#2037, C2×#70066, #10822784, … |
| maximal quotient of | #10698456, #10698463, #10698484, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2642);