Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67520 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C3×#347 ⋊ C2 |
| Sylow | C3 ⋊ #1355 |
88 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)(11,19)(14,15);(1,2,3)(4,5,6,11,7,9,15,17,8,12,14,19,16,10,13,18)Polycyclic presentation:
2^7,3|a^2=d,c^2=f,d^2=e,e^2=g,b^a=bc,c^a=ce,f^a=fg,c^b=cf,d^b=defg,e^b=eg,h^b=h^2,d^c=dg42 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1355, C2×#67520, #10706363, … |
| maximal normal subgroup of | D3×#1355, C2×#67520, #10706363, … |
| maximal quotient of | #10681964, #10682002, #10682355, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 96);