Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×#800 |
| Fitting | C22×C3×C16 ⋊ C2 |
| Sylow | C3 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(5,6,7)(8,9,14,20,19,23,10,13,12,16,17,22,11,15,18,21);(1,2)(3,4)(6,7)(9,13)(10,17)(11,19)(14,18)(15,22)(16,21)(20,23);(3,4);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10712250, #10712252, #10712257, … |
| maximal normal subgroup of | #10712250, #10712252, #10712257, … |
| maximal quotient of | C22×#4509, C22×#4503, C22×#4505, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14578);