Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#465 ⋊ C2 |
| Sylow | C3 ⋊ #3246 |
392 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(2,3)(4,6,7,10)(5,9,8,11);(1,2,3)(5,8)(9,11)(13,16)(14,19)(17,18);(4,5)(6,9)(7,8)(10,11);(5,8)(6,10)(12,13,15,18)(14,16,19,17)Polycyclic presentation:
2^7,3|a^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,f^c=fg,h^d=h^254 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3246, C2×#80640, #11668013, … |
| maximal normal subgroup of | D3×#3246, C2×#80640, #11668013, … |
| maximal quotient of | #10805062, #10805069, #10805558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13216);