Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C24 |
| direct product | C2×#4468 |
| Fitting | C2×C3×C22⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×#323 |
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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)(7,10,11,13)(8,12)(14,16,17,20,18,21,15,19);(4,5)(6,7)(8,10)(9,11)(12,13)(14,15)(16,20)(17,18)(19,21);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10685688, C4×#4468, #10685696, … |
| maximal normal subgroup of | #10685688, C4×#4468, #10685696, … |
| maximal quotient of | C2×#67479, C2×#67480, #10683137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2494);