Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | A4×#102 |
| unambiguous semidirect product | (C22×#102)⋊C3 |
| Fitting, Sylow | C22×#102 ⋊ C3 |
262 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 42 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) = 48 |
A minimal faithful permutation representation — 2 generators on 16 points:
(6,7,8)(10,13)(11,16)(14,15);(1,4,3,2)(5,8)(6,7)(9,10)(11,13)(12,15)(14,16)56 conjugacy classes — view the full character table.
| maximal subgroup of | C2×A4×#102, A4×#416, A4×#418, … |
| maximal normal subgroup of | C2×A4×#102, A4×#416, A4×#418, … |
| maximal quotient of | A4×D4⋊C8, #17507⋊C3, A4×#327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5811);