Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4883 |
| Fitting | C2×C3×#107 ⋊ C2 |
| Sylow | C3 ⋊ C2×#466 |
616 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 616 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:
(3,4,5)(6,7,8,9)(11,14)(12,17)(15,16);(10,11,12,15,13,16,17,14);(1,2)(4,5)(7,9);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10712124, #10712129, #10712195, … |
| maximal normal subgroup of | #10712124, #10712129, #10712195, … |
| maximal quotient of | C2×#68576, C2×#68578, C2×#68580, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11723);