Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×H(3,ℤ/4) ⋊ C2 |
| Sylow | C3 ⋊ #1909 |
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 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)(5,11)(6,15)(8,22)(9,20)(10,24)(12,27)(13,18)(14,28)(16,32)(17,31)(19,23)(21,26)(25,34)(29,35)(30,33);(4,6,8,16,9,17,23,33)(5,10,12,14,13,25,21,29)(7,15,22,32,20,31,19,30)(11,24,27,28,18,34,26,35);(2,3)(4,5)(6,14)(7,18,20,11)(8,21)(9,13)(10,16)(12,23)(15,28,31,35)(17,29)(19,26,22,27)(24,30,34,32)(25,33)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,d^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1909, C2×#68712, #10797171, … |
| maximal normal subgroup of | D3×#1909, C2×#68712, #10797171, … |
| maximal quotient of | #10690681, #10690686, #10690701, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1288);