Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1412 |
94 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3)(4,6,8,14)(5,9)(7,16,17,15)(10,13)(11,18)(12,19);(2,3)(4,5)(6,13,15,19)(7,11,17,10)(8,12)(9,14,18,16)Polycyclic presentation:
2^7,3|a^2=d,b^2=f,c^2=fg,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg30 conjugacy classes — view the full character table.
| maximal subgroup of | #10683027, #10683028, #10683030, … |
| maximal normal subgroup of | #10683027, #10683028, #10683030, … |
| maximal quotient of | #10682578, #10682596, #10682724, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 360);