Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#5244 |
| Fitting | C2×C3×H(5,𝔽2) ⋊ C2 |
| Sylow | C3 ⋊ C2×B(4,𝔽2) |
1018 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 165 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 — 4 generators on 13 points:
(3,4,5)(6,7)(8,10)(9,11)(12,13);(1,2)(8,12)(10,13);(1,2)(4,5)(7,10)(11,13);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10712444, #10712450, #10712458, … |
| maximal normal subgroup of | #10712444, #10712450, #10712458, … |
| maximal quotient of | C2×#71845, C2×#71846, C2×#71892, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16685);