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 ⋊ #2087 |
224 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 85 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)(17,22)(18,20)(21,23);(2,3)(4,5)(6,7)(8,10,12,11)(9,13,14,15)(16,18,19,20)(17,21,23,22);(2,3)(8,9)(10,15)(11,13)(12,14)(16,17,20,21,19,23,18,22)Polycyclic presentation:
2^7,3|a^2=e,b^2=d,c^2=dg,e^2=g,b^a=bd,c^a=ce,h^a=h^2,c^b=cf,h^b=h^2,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2087, C2×#68808, #10824249, … |
| maximal normal subgroup of | D3×#2087, C2×#68808, #10824249, … |
| maximal quotient of | #10700102, #10700112, #10700139, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1384);