Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4 |
| direct product | C2×#4939 |
| Fitting | C22×C3×C42 ⋊ C2 |
| Sylow | C3 ⋊ C2×#390 |
1360 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 1360 conjugacy classes of subgroups — too many to draw. Only its 381 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)(10,12,13,11)(15,17);(6,7,8,9)(10,11,13,12);(4,5)(7,9)(11,12)(14,15)(16,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#67479, #10683171, #10683173, … |
| maximal normal subgroup of | C2×#67479, #10683171, #10683173, … |
| maximal quotient of | C2×#71535, C2×#71537, C4×#4939, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14643);