Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#510 |
| Fitting | C3×#510 ⋊ C2 |
| Sylow | C3 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 35 points:
(2,8)(7,22)(9,24)(10,20)(11,28)(15,27)(23,26)(25,31)(33,34,35);(1,3,6,14)(2,7,8,22)(4,16,19,32)(5,21,17,13)(9,25,24,31)(10,26,20,23)(11,27,28,15)(12,29,30,18);(1,2)(3,11)(4,15)(5,20)(6,8)(7,12)(9,18)(10,17)(13,31)(14,28)(16,26)(19,27)(21,25)(22,30)(23,32)(24,29);(34,35)48 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2180, #10948650, D3×#2191, … |
| maximal normal subgroup of | D3×#2180, #10948650, D3×#2191, … |
| maximal quotient of | D3×#2141, D3×#2139, D3×#2159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14614);