Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1305 |
200 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 61 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 — 2 generators on 19 points:
(1,2,3)(4,6)(5,8,9,10)(7,11)(13,16)(14,18);(2,3)(4,5)(6,10)(7,9)(8,11)(12,13,14,17,15,16,18,19)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,d^2=f,b^a=bc,c^a=cf,e^a=eg,h^a=h^2,c^b=cg,d^b=df54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1305, C2×#67626, #10685519, … |
| maximal normal subgroup of | D3×#1305, C2×#67626, #10685519, … |
| maximal quotient of | #10681758, #10681761, #10681762, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 202);