Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D4×#215 |
| Fitting | C3×D4×Q8 ⋊ C2 |
| Sylow | C3 ⋊ D4×SD16 |
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 149 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 — 4 generators on 15 points:
(1,2,3)(8,9,11,13)(10,15,14,12);(2,3)(9,12)(10,14)(13,15);(5,7);(4,5)(6,7)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10784542, #10784550, #10784557, … |
| maximal normal subgroup of | #10784542, #10784550, #10784557, … |
| maximal quotient of | #10784648, #10784663, #10784678, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16137);