Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C3×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C3 ⋊ #3265 |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(9,13)(10,15)(12,14);(2,3)(5,7);(8,9,11,14)(10,13,15,12);(4,5)(6,7)(9,12)(10,15)(13,14)Polycyclic presentation:
2^7,3|b^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=de,e^b=eg,h^c=h^2,e^d=eg51 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3265, C2×#83953, #11670259, … |
| maximal normal subgroup of | D3×#3265, C2×#83953, #11670259, … |
| maximal quotient of | #10784543, #10784663, #10784798, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 16529);