Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#5075 |
| Sylow | C3 ⋊ C2×#460 |
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 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)(7,9)(11,14)(12,17)(15,16);(1,2)(6,7,8,9);(1,2)(4,5)(10,11,13,16)(12,14,17,15);(1,2)66 conjugacy classes — view the full character table.
| maximal subgroup of | #10689952, #10689958, #10689959, … |
| maximal normal subgroup of | #10689952, #10689958, #10689959, … |
| maximal quotient of | C2×#71272, C2×#71286, C2×#71308, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15744);