Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×#137 ⋊ C2 |
| Sylow | C3 ⋊ #2004 |
394 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 75 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) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(5,7)(11,21)(13,22)(14,19)(17,20);(1,2,3)(8,10,12,18)(9,13,15,22)(11,20,21,17)(14,23,19,16);(4,5)(6,7)(8,9)(10,16)(11,19)(12,15)(13,17)(14,21)(18,23)(20,22)Polycyclic presentation:
2^7,3|b^2=g,d^2=g,b^a=bd,c^a=ce,d^a=dg,f^a=fg,c^b=cf,d^b=dg,d^c=dg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2004, C2×#72106, #10822092, … |
| maximal normal subgroup of | D3×#2004, C2×#72106, #10822092, … |
| maximal quotient of | #10695394, #10695408, #10695450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4682);