Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68629 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2084 |
230 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 95 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) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(5,7)(8,11,12,10)(9,13,14,15)(17,21)(19,23)(20,22);(2,3)(8,10,12,11)(9,13,14,15)(16,17,18,20)(19,21,23,22);(4,5,6,7)(8,9)(10,15)(11,13)(12,14)(17,20)(21,22)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,c^2=dg,f^2=g,b^a=bd,c^a=ce,c^b=cf,f^b=fg,h^b=h^2,f^c=fg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | #10684246, #10684247, #10684260, … |
| maximal normal subgroup of | #10684246, #10684247, #10684260, … |
| maximal quotient of | #10700105, #10700110, #10700122, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1216);