Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D3×B(4,𝔽2) |
| Fitting | C3×B(4,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 11 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 4 generators on 11 points:
(1,2,3)(4,6)(5,8)(7,10)(9,11);(4,5)(6,8)(7,9)(10,11);(8,11);(2,3)48 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12882);