Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ #1733 |
404 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 137 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)(10,17)(13,21)(16,22)(18,23);(1,2,3)(8,10)(9,13,15,21)(11,18)(12,17)(14,16,19,22)(20,23);(4,5,6,7)(8,9)(10,16)(11,19)(12,15)(13,18)(14,20)(17,22)(21,23)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,d^2=g,b^a=bd,d^a=dg,f^a=fg,c^b=cg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1733, C2×#68753, #10792576, … |
| maximal normal subgroup of | D3×#1733, C2×#68753, #10792576, … |
| maximal quotient of | #10684624, #10684630, #10684633, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1329);