Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C3 ⋊ #1375 |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(5,7)(9,14,17,15)(11,19)(16,22,23,21)(18,20);(2,3)(4,5)(6,7)(8,9,11,16,12,14,20,21,13,17,19,23,10,15,18,22)Polycyclic presentation:
2^7,3|a^2=d,b^2=e,c^2=g,d^2=f,f^2=g,b^a=bc,e^a=eg,h^a=h^2,d^b=dg84 conjugacy classes — view the full character table.
| maximal subgroup of | #10681944, #10681945, #10681964, … |
| maximal normal subgroup of | #10681944, #10681945, #10681964, … |
| maximal quotient of | #10682017, #10682029, #10682036, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 239);