Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×#508 |
| Fitting | C3×#508 ⋊ C2 |
| Sylow | C3 ⋊ C2×#508 |
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 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:
(1,4,7,6)(2,9,11,21)(3,13,15,22)(5,16,20,19)(8,23,25,24)(10,17,27,31)(12,28,29,26)(14,18,30,32)(33,34,35);(1,3)(2,8)(4,13)(5,18)(6,22)(7,15)(9,23)(10,26)(11,25)(12,17)(14,19)(16,30)(20,32)(21,24)(27,28)(29,31);(1,2)(3,12)(4,9)(5,17)(6,21)(7,11)(8,14)(10,19)(13,28)(15,29)(16,27)(18,23)(20,31)(22,26)(24,32)(25,30);(34,35)66 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1417, #10715640, D3×#1418, … |
| maximal normal subgroup of | D3×#1417, #10715640, D3×#1418, … |
| maximal quotient of | D3×#2138, D3×#2158, C4×D3×D16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14605);