Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2210 |
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(9,14)(11,19)(12,18)(13,21)(15,16)(17,23)(20,22);(2,3)(4,5,6,7)(9,13)(14,21)(15,22)(16,20);(5,7)(8,9)(10,13)(11,14)(12,20)(15,19)(16,18)(17,21)(22,23)Polycyclic presentation:
2^7,3|b^2=dg,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^b=h^2,e^c=ef,f^c=fg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2210, C2×#71463, #10949447, … |
| maximal normal subgroup of | D3×#2210, C2×#71463, #10949447, … |
| maximal quotient of | #10709315, #10709347, #10709377, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4039);