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 ⋊ #3310 |
450 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(6,11)(8,10);(2,3)(13,18)(14,15)(17,19);(2,3)(4,6)(5,8)(7,11)(9,10)(12,14,16,15)(13,17,19,18);(2,3)(4,5,7,9)(6,10,11,8)(12,13)(14,17)(15,18)(16,19)Polycyclic presentation:
2^7,3|a^2=e,b^2=g,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×#3310, C2×#80685, #11671965, … |
| maximal normal subgroup of | D3×#3310, C2×#80685, #11671965, … |
| maximal quotient of | #10810733, #10811481, #10812237, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13261);