Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#342 ⋊ C2 |
| Sylow | C3 ⋊ #2029 |
466 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(16,19);(4,6,7,11)(5,8,9,10)(12,14)(13,16)(15,18)(17,19);(2,3)(4,5,7,9)(6,10,11,8)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=d,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10707905, #10707910, #10707923, … |
| maximal normal subgroup of | #10707905, #10707910, #10707923, … |
| maximal quotient of | #10698156, #10698158, #10698161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1547);