Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C3×#354 ⋊ C2 |
| Sylow | C3 ⋊ #1406 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 19 points:
(2,3)(5,9)(6,13)(7,16)(10,12)(14,15)(17,18);(1,2,3)(4,5,6,11)(7,10,13,18)(8,12,14,19)(9,15,17,16)Polycyclic presentation:
2^7,3|a^2=d,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^2,d^c=dfg,e^d=eg27 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1406, C2×#67544, #10715473, … |
| maximal normal subgroup of | D3×#1406, C2×#67544, #10715473, … |
| maximal quotient of | #10682565, #10682607, #10682693, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 120);