Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of Dic6 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C4×ΓL(1,𝔽25) |
| Fitting | C2×C3×C4×C8 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 357 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 357 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(3,4,5)(10,11,12,15,13,14,16,17);(1,2)(4,5)(11,14)(15,17);(6,7,8,9);(1,2)144 conjugacy classes — view the full character table.
| maximal subgroup of | #10684567, #10684574, #10684579, … |
| maximal normal subgroup of | #10684567, #10684574, #10684579, … |
| maximal quotient of | C2×C8×ΓL(1,𝔽25), C2×#68069, C2×#68048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11026);