Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#343 ⋊ C2 |
| Sylow | C3 ⋊ #2039 |
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 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) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(1,2)(4,6,7,5)(9,13)(10,11)(14,15);(2,3)(4,5)(6,7)(8,9)(10,14)(11,13)(12,15);(2,3)(5,6)(8,9)(10,13)(11,14)(12,15)Polycyclic presentation:
2^7,3|c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,f^b=fg,h^b=h^2,e^c=eg,f^c=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10707512, #10707514, #10707526, … |
| maximal normal subgroup of | #10707512, #10707514, #10707526, … |
| maximal quotient of | #10698512, #10698531, #10698536, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1552);