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 ⋊ #2187 |
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7);(2,3)(9,13)(10,17)(11,18)(14,15)(16,22)(19,23)(20,21);(2,3)(4,5)(6,7)(8,9,12,16)(10,13,19,22)(11,20,18,15)(14,23,21,17)Polycyclic presentation:
2^7,3|a^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 | #10707290, #10707291, #10707296, … |
| maximal normal subgroup of | #10707290, #10707291, #10707296, … |
| maximal quotient of | #10707303, #10707647, #10708407, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1686);