Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#509 ⋊ C2 |
| Sylow | C3 ⋊ #2193 |
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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 — 3 generators on 35 points:
(2,3)(4,6,10,17)(5,12,14,29)(7,16,21,32)(8,22,9,15)(11,24,25,35)(13,28,23,27)(18,31,20,34)(19,33,30,26);(1,2,3)(4,5)(6,12)(7,19)(8,13)(9,23)(10,14)(11,18)(15,27)(16,33)(17,29)(20,25)(21,30)(22,28)(24,31)(26,32)(34,35);(5,11)(6,15)(7,18)(8,9)(12,26)(13,30)(14,25)(16,32)(17,22)(19,23)(20,21)(24,27)(28,35)(29,33)Polycyclic presentation:
2^7,3|c^2=g,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,d^b=df,f^b=fg,e^c=eg,h^c=h^239 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2193, C2×#71518, #10949138, … |
| maximal normal subgroup of | D3×#2193, C2×#71518, #10949138, … |
| maximal quotient of | #10707321, #10707326, #10707665, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4094);