Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4776 |
| Fitting | C2×C3×#102 ⋊ C2 |
| Sylow | C3 ⋊ C2×#450 |
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,8,9,7)(10,11)(12,17)(13,14)(15,16);(1,2)(6,7)(8,9)(11,15)(12,16)(14,17);(4,5)(6,7)(8,9)(11,14)(15,17);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10800764, C4×#4776, #10800838, … |
| maximal normal subgroup of | #10800764, C4×#4776, #10800838, … |
| maximal quotient of | C2×#68286, C2×#68290, C2×#68295, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11320);