Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×Q8⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #1477 |
264 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 83 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:
(1,2)(13,17)(16,19);(2,3)(12,13)(14,19)(15,17)(16,18);(4,5,6,8,7,9,10,11)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,c^b=cf,d^b=df,h^b=h^2,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1477, C2×#68230, #10761558, … |
| maximal normal subgroup of | D3×#1477, C2×#68230, #10761558, … |
| maximal quotient of | #10683180, #10683191, #10683198, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 806);