Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#5238 |
| Fitting | C22×C3×#41 ⋊ C2 |
| Sylow | C3 ⋊ C2×#449 |
812 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 181 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:
(3,4,5)(6,7)(8,9)(10,12,13,17)(11,15,16,14);(1,2)(10,11)(12,15)(13,16)(14,17);(1,2)(4,5)(7,9)(11,14)(12,17)(15,16);(1,2)78 conjugacy classes — view the full character table.
| maximal subgroup of | #10691506, #10691508, #10800795, … |
| maximal normal subgroup of | #10691506, #10691508, #10800795, … |
| maximal quotient of | C2×#71888, C2×#71886, C2×#71884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16655);