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 ⋊ #1849 |
212 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3)(4,5,6,7)(10,18)(14,22)(17,23)(19,20);(8,10,11,19,13,18,12,20)(9,14,15,17,16,22,21,23);(2,3)(5,7)(8,9,12,15,13,16,11,21)(10,17,20,22,18,23,19,14)Polycyclic presentation:
2^7,3|a^2=f,b^2=d,c^2=e,d^2=g,f^2=g,b^a=bd,c^a=ce,d^a=dg,h^a=h^2,c^b=cg72 conjugacy classes — view the full character table.
| maximal subgroup of | #10689579, #10689580, #10699324, … |
| maximal normal subgroup of | #10689579, #10689580, #10699324, … |
| maximal quotient of | #10688936, #10688940, #10688943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 2418);