Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5134 |
| Fitting | C22×C3×M16 ⋊ C2 |
| Sylow | C3 ⋊ C2×#468 |
544 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 544 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) = 17 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 17 points:
(1,2)(3,4,5)(6,7)(8,9)(11,15)(14,17);(1,2)(10,11,12,14,13,15,16,17);(4,5)(7,9)(11,14)(12,16)(15,17);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10801809, C4×#5134, #10801846, … |
| maximal normal subgroup of | #10801809, C4×#5134, #10801846, … |
| maximal quotient of | C2×#70867, C2×#70872, C2×#70869, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16345);