Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#339 ⋊ C2 |
| Sylow | C3 ⋊ #2038 |
278 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2)(4,6,7,5)(9,14)(11,20)(13,21)(15,16)(17,19)(22,23);(2,3)(4,5)(6,7)(8,10,12,18)(9,13,16,23)(11,19,20,17)(14,22,15,21);(2,3)(5,6)(8,9)(10,13)(11,14)(12,16)(15,20)(17,21)(18,23)(19,22)Polycyclic presentation:
2^7,3|b^2=g,c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,e^b=eg,h^b=h^2,e^c=eg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2038, C2×#68734, #10822784, … |
| maximal normal subgroup of | D3×#2038, C2×#68734, #10822784, … |
| maximal quotient of | #10698472, #10698479, #10698500, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1310);