Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#336 ⋊ C2 |
| Sylow | C3 ⋊ #1752 |
360 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 129 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) = 192 |
A minimal faithful permutation representation — 3 generators on 19 points:
(2,3)(12,14,16,19,15,13,17,18);(1,2,3)(4,5,6,7)(9,11)(13,14)(18,19);(8,9)(10,11)(12,13,16,18,15,14,17,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=f,c^2=e,e^2=g,b^a=bd,c^b=cg,h^c=h^296 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1752, C2×#68648, #10792783, … |
| maximal normal subgroup of | D3×#1752, C2×#68648, #10792783, … |
| maximal quotient of | #10685655, #10685659, #10685681, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1224);