Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#563 ⋊ C2 |
| Sylow | C3 ⋊ #2201 |
226 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 45 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:
(1,4,6,17)(2,8,10,24)(3,12,14,15)(5,18,19,16)(7,20,21,22)(9,23,25,32)(11,26,27,31)(13,29,30,28)(33,34,35);(1,3,6,14)(2,7,10,21)(4,15,17,12)(5,13,19,30)(8,22,24,20)(9,11,25,27)(16,29,18,28)(23,31,32,26);(1,2)(3,11)(4,8)(5,9)(6,10)(7,13)(12,26)(14,27)(15,31)(16,23)(17,24)(18,32)(19,25)(20,28)(21,30)(22,29)(34,35)Polycyclic presentation:
2^7,3|b^2=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^2,c^b=cg,e^b=efg,d^c=df,e^d=eg36 conjugacy classes — view the full character table.
| maximal subgroup of | #10715930, #10715932, #10715937, … |
| maximal normal subgroup of | #10715930, #10715932, #10715937, … |
| maximal quotient of | #10707245, #10707279, #10707414, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 4534);