Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×#4676 |
| Fitting | C2×C3×#95 ⋊ C2 |
| Sylow | C3 ⋊ C2×#396 |
908 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 245 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)(11,13)(14,15)(16,17);(7,9)(10,11)(12,13)(14,15,16,17);(1,2)(4,5)(7,9)(11,13)(15,17);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10717046, C4×#4676, #10720833, … |
| maximal normal subgroup of | #10717046, C4×#4676, #10720833, … |
| maximal quotient of | C2×#69428, C2×#69409, C2×#69416, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5948);