Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#421 ⋊ C2 |
| Sylow | C3 ⋊ #1976 |
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 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:
(1,2)(4,7,8,18,9,19,21,32)(5,11,13,17,12,25,20,31)(6,14,16,28,15,27,29,33)(10,22,23,26,24,34,30,35);(2,3)(4,6)(5,10,12,24)(7,14)(8,16)(9,15)(11,22,25,34)(13,23,20,30)(17,26,31,35)(18,28)(19,27)(21,29)(32,33);(4,5)(6,10,15,24)(7,17)(8,20)(9,12)(11,18)(13,21)(14,26,27,35)(16,30,29,23)(19,31)(22,33,34,28)(25,32)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=e,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,d^b=dg,f^b=fg,h^b=h^2,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1976, C2×#70397, #10799163, … |
| maximal normal subgroup of | D3×#1976, C2×#70397, #10799163, … |
| maximal quotient of | #10694105, #10694109, #10694112, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2973);