Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×Q8×A4 |
| Fitting, Sylow | C22×C4×Q8 ⋊ C3 |
394 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 96 |
A minimal faithful permutation representation — 3 generators on 16 points:
(6,7,8)(9,11,12,16)(10,13,14,15);(5,8)(6,7)(9,10,12,14)(11,15,16,13);(1,2,3,4)80 conjugacy classes — view the full character table.
| maximal subgroup of | A4×Q8⋊C8, C4×A4×SD16, C4×A4×Q16, … |
| maximal normal subgroup of | A4×Q8⋊C8, C4×A4×SD16, C4×A4×Q16, … |
| maximal quotient of | C4×A4×C4⋊C4, A4×#387, A4×#389, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18150);