Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×C22⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ #2186 |
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 53 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)(5,7)(8,10,12,13)(9,15,16,21)(11,17,20,18)(14,19,22,23);(2,3)(8,9)(10,15)(11,19)(12,16)(13,21)(14,18)(17,22)(20,23);(2,3)(4,5)(6,7)(9,14)(10,13)(11,18)(15,23)(16,22)(17,20)(19,21)Polycyclic presentation:
2^7,3|c^2=g,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^2,d^b=df,f^b=fg,h^b=h^269 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2186, C2×#69109, #10948968, … |
| maximal normal subgroup of | D3×#2186, C2×#69109, #10948968, … |
| maximal quotient of | #10707297, #10707641, #10708401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1685);