Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×#361 ⋊ C2 |
| Sylow | C3 ⋊ #2221 |
148 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 43 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:
(1,2)(4,6)(5,13)(7,18)(8,22)(9,17)(10,19)(11,23)(12,27)(14,31)(15,29)(16,30)(20,33)(21,32)(24,35)(25,28)(26,34);(2,3)(4,5,12,25,9,15,21,26,10,16,20,24,8,14,7,11)(6,13,27,28,17,29,32,34,19,30,33,35,22,31,18,23);(5,11)(6,17)(7,12)(8,9)(13,28)(14,25)(15,24)(16,26)(18,32)(19,22)(20,21)(23,29)(30,35)(31,34)Polycyclic presentation:
2^7,3|b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^b=h^2,e^c=eg,h^c=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2221, C2×#69260, #10949763, … |
| maximal normal subgroup of | D3×#2221, C2×#69260, #10949763, … |
| maximal quotient of | #10709392, #10709409, #10709443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1836);