Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#4536 |
| Sylow | C3 ⋊ C2×AΣL(1,𝔽16) |
438 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 13 points:
(3,4,5)(7,10)(11,12);(4,5)(6,7)(8,12,13,10)(9,11);(1,2)54 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4536, Dic3×AΣL(1,𝔽16), #10710334, … |
| maximal normal subgroup of | C4×#4536, Dic3×AΣL(1,𝔽16), #10710334, … |
| maximal quotient of | C2×#67622, C2×#67636, #10704437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4244);