Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #2884⋊C3 |
| Fitting, Sylow | #2884 ⋊ C3 |
191 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 191 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,3,4,14)(2,7,8,11)(5,27,18,29,16,28,15,13,17,12,6,30)(9,26,24,25,22,31,21,20,23,19,10,32);(1,24,4,23)(2,18,8,17)(3,31)(5,10,15,22)(6,21,16,9)(7,30)(11,28)(12,26)(13,19)(14,32)(20,29)(25,27)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^b=eh,f^c=gh,g^c=fgh,g^f=gh43 conjugacy classes — view the full character table.
| maximal subgroup of | #33349⋊C3, #33351⋊C3, #33360⋊C3, … |
| maximal normal subgroup of | #33349⋊C3, #33351⋊C3, #33360⋊C3, … |
| maximal quotient of | #17352⋊C3, #17353⋊C3, #17425⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5806);