Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#875 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C22×#124 |
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 19 points:
(1,2)(3,4)(5,6,7)(8,10,11,9)(12,14,15,18)(13,17,16,19);(8,9,11,10)(13,16)(17,19);(6,7)(9,10)(12,13)(14,17)(15,16)(18,19);(3,4);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10686537, #10686653, #10701729, … |
| maximal normal subgroup of | #10686537, #10686653, #10701729, … |
| maximal quotient of | C22×#4936, C22×#4940, C22×#4939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18251);