Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#806 |
| Fitting | C3×C4×C22⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 117 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 — 3 generators on 15 points:
(1,2,3)(8,10)(9,12,13,14)(11,15);(2,3)(8,9)(10,14)(11,13)(12,15);(4,5,6,7)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10685727, C8×#806, #10685732, … |
| maximal normal subgroup of | #10685727, C8×#806, #10685732, … |
| maximal quotient of | C4×#4468, C4×#4469, #10685698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2031);