Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#344 ⋊ C2 |
| Sylow | C3 ⋊ #1891 |
342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 342 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) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2)(4,6)(5,9)(7,15)(8,13)(10,12)(11,19)(14,16)(17,18);(4,5,7,11,8,10,16,18)(6,9,15,19,13,12,14,17);(2,3)(4,5,7,11,8,10,16,18)(6,12,14,19,13,9,15,17)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,f^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^2,e^b=eg,d^c=dg,f^c=fg,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1891, C2×#69036, #10796840, … |
| maximal normal subgroup of | D3×#1891, C2×#69036, #10796840, … |
| maximal quotient of | #10689871, #10689876, #10689881, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1612);