Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#4707 |
| Fitting | C2×C3×#97 ⋊ C2 |
| Sylow | C3 ⋊ C2×C4×M16 |
656 conjugacy classes of subgroups; only the 341 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 341 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);(6,7,8,9)(11,14)(15,17);(1,2)(4,5)(11,14)(15,17);(1,2)120 conjugacy classes — view the full character table.
| maximal subgroup of | #10684604, #10684610, #10684816, … |
| maximal normal subgroup of | #10684604, #10684610, #10684816, … |
| maximal quotient of | C2×#68067, C2×#68070, C2×#68072, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11060);