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 ⋊ #3343 |
376 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(6,11)(9,10);(2,3)(4,7,8,5)(6,10,11,9)(12,13)(14,19)(15,17)(16,18);(2,3)(4,6)(5,9)(7,10)(8,11)(13,17)(16,19);(2,3)(4,5,8,7)(6,10,11,9)(13,16)(14,18)(17,19)Polycyclic presentation:
2^7,3|a^2=e,c^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,h^b=h^2,f^c=fg,h^c=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3343, C2×#80651, #11673854, … |
| maximal normal subgroup of | D3×#3343, C2×#80651, #11673854, … |
| maximal quotient of | #10811481, #10811541, #10812887, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13227);