Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×(C2×S4)⋊C4 |
| Fitting | C24×C4 ⋊ D3 |
711 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 711 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(3,4,6)(7,8)(9,10)(11,12,13,14);(4,5)(8,10);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #11711146, C4×(C2×S4)⋊C4, #11711692, … |
| maximal normal subgroup of | #11711146, C4×(C2×S4)⋊C4, #11711692, … |
| maximal quotient of | C2×A4⋊#95, C4×(C2×S4)⋊C4, #11711694, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18059);