Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C3×C4×C16 ⋊ C2 |
| Sylow | C3 ⋊ #2169 |
162 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 162 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)(8,10,12,19,13,14,17,22,11,18,20,23,21,9,15,16);(2,3)(5,7)(9,14)(10,18)(16,22)(19,23);(2,3)(4,5)(6,7)(8,9,12,16,13,10,17,19,11,14,20,22,21,18,15,23)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2,c^b=cg,h^b=h^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #10682627, #10682629, #10706897, … |
| maximal normal subgroup of | #10682627, #10682629, #10706897, … |
| maximal quotient of | #10706905, #10706976, #10706994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1631);