Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×H(3,𝔽4) ⋊ C2 |
| Sylow | C3 ⋊ #2202 |
248 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(2,7)(4,13)(6,15)(8,16)(9,10)(12,14)(17,18,19);(2,6)(3,11)(4,13)(7,15)(8,10)(9,16);(1,2)(3,6)(4,7)(5,10)(8,11)(9,13)(12,15)(14,16)(18,19)Polycyclic presentation:
2^7,3|d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,h^a=h^2,d^b=dg,e^b=efg,d^c=df,e^c=eg,e^d=eg36 conjugacy classes — view the full character table.
| maximal subgroup of | #10715917, #10715918, #10715924, … |
| maximal normal subgroup of | #10715917, #10715918, #10715924, … |
| maximal quotient of | #10707250, #10707425, #10707518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4527);