Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#4869 |
| Fitting | C2×C3×#106 ⋊ C2 |
| Sylow | C3 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,7,8,9)(11,16)(12,15)(14,17);(1,2)(10,11,15,16,13,17,12,14);(4,5)(11,14)(12,15)(16,17);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710456, #10710458, #10711923, … |
| maximal normal subgroup of | #10710456, #10710458, #10711923, … |
| maximal quotient of | C2×#68518, C2×#68521, C2×#68525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11681);