Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1990 |
300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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) = 384 |
A minimal faithful permutation representation — 3 generators on 23 points:
(2,3)(8,10,11,15)(9,12,13,14);(1,2,3)(4,6,7,5)(16,17,18,20,19,21,22,23);(4,5,7,6)(8,9,11,13)(10,14,15,12)(17,20)(18,22)(21,23)Polycyclic presentation:
2^7,3|a^2=f,b^2=de,c^2=ef,d^2=g,b^a=bd,c^a=cef,d^a=dg,h^c=h^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1990, C2×#68803, #10799745, … |
| maximal normal subgroup of | D3×#1990, C2×#68803, #10799745, … |
| maximal quotient of | #10695192, #10695208, #10695250, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1379);