Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×C4×C16 ⋊ C2 |
| Sylow | C3 ⋊ #2246 |
216 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);(8,9,14,20,11,15,18,21,12,16,22,23,17,19,10,13);(2,3)(5,7)(9,13)(10,14)(11,17)(15,23)(16,21)(18,22)(19,20)Polycyclic presentation:
2^7,3|b^2=df,c^2=e,d^2=fg,f^2=g,b^a=bd,c^a=ce,d^a=df,f^a=fg,h^a=h^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #10682819, #10682821, #10682831, … |
| maximal normal subgroup of | #10682819, #10682821, #10682831, … |
| maximal quotient of | #10709840, #10709873, #10709899, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 1636);