Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #2008 |
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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:
(1,2,3)(5,11)(7,8)(10,14)(12,13)(15,17)(18,19);(2,3)(4,6)(5,10)(7,17)(8,15)(9,16)(11,19)(12,14)(13,18);(4,5)(6,14)(7,12)(8,11)(9,13)(10,15)(16,19)(17,18)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,c^b=cf,d^b=dg,h^b=h^2,d^c=dg,e^c=eg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2008, C2×#72099, #10822192, … |
| maximal normal subgroup of | D3×#2008, C2×#72099, #10822192, … |
| maximal quotient of | #10695493, #10695507, #10695521, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4675);