Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#419 ⋊ C2 |
| Sylow | C3 ⋊ #1902 |
304 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 79 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)(4,7)(5,12)(6,16)(8,21)(9,20)(10,22)(11,25)(13,29)(14,28)(15,30)(17,34)(18,33)(19,23)(24,32)(26,35)(27,31);(1,2,3)(4,6,8,17,10,18,9,24)(5,11,13,15,14,27,23,26)(7,16,21,34,22,33,20,32)(12,25,29,30,28,31,19,35);(4,5)(6,15)(7,19,22,29)(8,23)(9,13)(10,14)(11,17)(12,21,28,20)(16,31,33,25)(18,26)(24,27)(30,32,35,34)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^b=eg,d^c=dg,e^c=eg,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1902, C2×#70349, #10797056, … |
| maximal normal subgroup of | D3×#1902, C2×#70349, #10797056, … |
| maximal quotient of | #10690595, #10690602, #10690623, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2925);