Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4742 |
| Fitting | C2×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ C2×#458 |
794 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 794 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) = 21 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 21 points:
(1,2)(3,4,5)(7,12)(8,14,15,21)(10,16)(11,18,20,19);(1,2)(6,8)(7,11)(9,15)(10,14)(12,20)(13,19)(16,21)(17,18);(4,5)(6,7)(8,11)(9,12)(10,17)(13,16)(14,18)(15,20)(19,21);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | #10712453, #10712455, #10712467, … |
| maximal normal subgroup of | #10712453, #10712455, #10712467, … |
| maximal quotient of | C2×#68288, C2×#68110, C2×#68290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11261);