Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #548⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1 |
| direct product | M16×SL(2,𝔽3) |
| unambiguous semidirect product | (Q8×M16)⋊C3 |
| Fitting, Sylow | Q8×M16 ⋊ C3 |
138 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 16 points:
(2,5)(6,8)(10,11,13)(14,16,15);(1,2,3,6,4,5,7,8)(9,13,12,15)(10,16,14,11)70 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5826);