Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4 |
| direct product | C22×#872 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C22×#117 |
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 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:
(5,6,7)(8,9,10,11)(13,17)(16,19);(1,2)(3,4)(12,14,15,18)(13,16,17,19);(6,7)(12,13)(14,16)(15,17)(18,19);(3,4);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10686519, #10700406, #10700431, … |
| maximal normal subgroup of | #10686519, #10700406, #10700431, … |
| maximal quotient of | C22×#4932, C22×C4×(C2×D3)⋊C4, C22×C4×Dic3⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18249);