Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #69507 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #2025 |
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(5,7)(17,21)(19,23)(20,22);(4,5)(6,7)(8,10,11,15)(9,12,13,14)(17,20)(21,22);(2,3)(8,9,11,13)(10,14,15,12)(16,17,18,20)(19,21,23,22)Polycyclic presentation:
2^7,3|a^2=d,b^2=dg,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,c^b=cf,e^c=eg60 conjugacy classes — view the full character table.
| maximal subgroup of | #10682771, #10682773, D3×#2025, … |
| maximal normal subgroup of | #10682771, #10682773, D3×#2025, … |
| maximal quotient of | #10698177, #10698187, #10698214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2215);