Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4518 |
| Fitting | C2×C3×M32 ⋊ C2 |
| Sylow | C3 ⋊ C2×#360 |
232 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 85 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 — 3 generators on 21 points:
(3,4,5)(6,8,16,14,11,17,9,15,12,18,19,21,10,13,20,7);(4,5)(6,7)(8,9)(10,14)(11,21)(12,15)(13,19)(16,17)(18,20);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10710434, C4×#4518, #10710479, … |
| maximal normal subgroup of | #10710434, C4×#4518, #10710479, … |
| maximal quotient of | C2×#67516, C2×#67517, #10704959, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4025);