Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4827 |
| Fitting | C2×C3×#104 ⋊ C2 |
| Sylow | C3 ⋊ C2×#454 |
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 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)(6,9,19,17,11,16,10,8)(7,12,14,21,15,20,13,18);(1,2)(6,8,11,17)(7,12,15,20)(9,10,16,19)(13,18,14,21);(4,5)(6,7)(8,12)(9,18)(10,14)(11,15)(13,19)(16,21)(17,20);(1,2)60 conjugacy classes — view the full character table.
| maximal subgroup of | #10801080, C4×#4827, #10801124, … |
| maximal normal subgroup of | #10801080, C4×#4827, #10801124, … |
| maximal quotient of | C2×#68292, C2×#68324, C2×#68298, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11563);