Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×Q8⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1493 |
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(13,14)(18,19);(1,2,3)(4,5,7,9)(6,11,10,8)(12,14,17,13)(15,18,16,19);(5,8)(6,10)(9,11)(12,13,16,18,17,14,15,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,d^2=f,e^2=g,b^a=bd,c^a=cg,d^a=df,c^b=cg,d^b=df,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1493, C2×#68240, #10761797, … |
| maximal normal subgroup of | D3×#1493, C2×#68240, #10761797, … |
| maximal quotient of | #10683549, #10683551, #10683554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 816);