Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | D8×#67 |
| Fitting | C22×C3×D8 ⋊ C2 |
| Sylow | C3 ⋊ D4×D8 |
620 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 141 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)(5,7);(2,3)(4,5)(6,7);(9,12)(10,15)(13,14);(8,9)(10,12)(11,14)(13,15)63 conjugacy classes — view the full character table.
| maximal subgroup of | #10951639, #10951643, #10951645, … |
| maximal normal subgroup of | #10951639, #10951643, #10951645, … |
| maximal quotient of | #10784530, #10784535, #10784545, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16414);