Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C22⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ #2169 |
162 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 162 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) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(8,10,12,19,13,14,17,22,11,18,20,23,21,9,15,16);(1,2,3)(5,7)(9,14)(10,18)(16,22)(19,23);(4,5)(6,7)(8,9,12,16,13,10,17,19,11,14,20,22,21,18,15,23)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,c^b=cg,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2169, C2×#69104, #10948362, … |
| maximal normal subgroup of | D3×#2169, C2×#69104, #10948362, … |
| maximal quotient of | #10706901, #10706971, #10706977, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1680);