Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 15 points:
(2,3)(4,6,7,5);(1,2,3)(9,12,14,13);(4,5,7,6)(8,9)(10,12)(11,14)(13,15)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,d^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | C4×D3×#104, C2×#68728, #10792908, … |
| maximal normal subgroup of | C4×D3×#104, C2×#68728, #10792908, … |
| maximal quotient of | #10685778, #10685783, #10685798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1304);