Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C3×#568 ⋊ C2 |
| Sylow | C3 ⋊ #2889 |
704 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 249 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:
(1,2,3)(7,18)(11,24)(15,29)(19,31)(22,28)(25,34)(30,32)(33,35);(4,7)(5,11)(6,15)(8,19)(9,18)(10,22)(12,24)(13,25)(14,28)(16,30)(17,29)(20,32)(21,31)(23,33)(26,34)(27,35);(2,3)(4,6,9,17)(5,10,12,14)(7,15,18,29)(8,20,21,16)(11,22,24,28)(13,27,26,23)(19,32,31,30)(25,35,34,33);(4,5,8,13,9,12,21,26)(6,14,16,27,17,10,20,23)(7,11,19,25,18,24,31,34)(15,28,30,35,29,22,32,33)Polycyclic presentation:
2^7,3|a^2=f,b^2=g,f^2=g,b^a=be,e^a=eg,f^b=fg,h^b=h^2,d^c=dg75 conjugacy classes — view the full character table.
| maximal subgroup of | #10804358, #10804360, #10804364, … |
| maximal normal subgroup of | #10804358, #10804360, #10804364, … |
| maximal quotient of | #10761009, #10761014, #10761098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16391);