Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4734 |
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#449 |
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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)(7,9)(10,13,17,16,14,15,12,11);(1,2)(6,7)(8,9)(10,12,14,17)(11,13,16,15);(4,5)(10,11)(12,13)(14,16)(15,17);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691507, #10691509, #10800799, … |
| maximal normal subgroup of | #10691507, #10691509, #10800799, … |
| maximal quotient of | C2×#68130, C2×#68134, C2×#68107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11184);