Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #2217 |
164 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 55 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);(2,3)(8,9,14,23,11,15,10,13,12,16,17,21,18,20,19,22);(4,5)(6,7)(9,13)(10,17)(11,18)(14,19)(15,23)(16,22)(20,21)Polycyclic presentation:
2^7,3|b^2=dfg,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2217, C2×#71072, #10949621, … |
| maximal normal subgroup of | D3×#2217, C2×#71072, #10949621, … |
| maximal quotient of | #10709401, #10709452, #10709520, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3648);