Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ #2168 |
164 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10,11,18,12,16,17,23,13,19,20,22,21,9,14,15);(5,7);(2,3)(4,5)(6,7)(8,9,11,15,12,10,17,18,13,16,20,23,21,19,14,22)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2168, C2×#71407, #10948355, … |
| maximal normal subgroup of | D3×#2168, C2×#71407, #10948355, … |
| maximal quotient of | #10706897, #10706958, #10706967, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3983);