Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #68807 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2083 |
230 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 89 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:
(1,2,3)(5,7)(8,11,12,10)(9,13,14,15)(17,20)(18,23)(21,22);(8,10,12,11)(9,13,14,15)(16,17)(18,20)(19,22)(21,23);(2,3)(4,5,6,7)(8,9)(10,15)(11,13)(12,14)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,c^2=d,f^2=g,b^a=bd,c^a=ce,h^a=h^2,c^b=cf,f^b=fg,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2083, C2×#70619, #10824170, … |
| maximal normal subgroup of | D3×#2083, C2×#70619, #10824170, … |
| maximal quotient of | #10700096, #10700101, #10700116, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3195);