Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1930 |
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(8,10,11,17,12,16,18,23)(9,14,13,19,15,22,20,21);(2,3)(4,6,7,5)(8,9,11,13,12,15,18,20)(10,14,17,19,16,22,23,21);(4,5,7,6)(9,13)(10,16)(11,18)(14,21)(15,20)(19,22)Polycyclic presentation:
2^7,3|a^2=f,b^2=df,c^2=d,d^2=g,b^a=bd,c^a=ce,d^a=dg,h^b=h^2,e^c=eg54 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1930, C2×#68982, #10797732, … |
| maximal normal subgroup of | D3×#1930, C2×#68982, #10797732, … |
| maximal quotient of | #10693414, #10693428, #10693498, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1558);