Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#323 ⋊ C2 |
| Sylow | C3 ⋊ #1471 |
322 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 65 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) = 96 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(12,14,16,15)(13,18,17,19);(1,2,3)(4,6)(5,8)(7,11)(9,10)(13,17)(14,15);(4,5)(6,10,11,8)(7,9)(12,13,15,19,16,17,14,18)Polycyclic presentation:
2^7,3|a^2=e,c^2=g,e^2=g,b^a=bd,d^a=df,c^b=cg,e^b=ef,h^c=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1471, C2×#68123, #10761167, … |
| maximal normal subgroup of | D3×#1471, C2×#68123, #10761167, … |
| maximal quotient of | #10683562, #10683575, #10683588, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 699);