Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #826 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1335 |
100 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)(5,10)(7,16)(8,13)(9,17)(11,19)(12,14)(15,18);(2,3)(4,5,7,12,9,13,19,15,10,6,14,16,8,17,18,11)Polycyclic presentation:
2^7,3|a^2=d,c^2=eg,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^2,c^b=ce,e^b=eg72 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1335, C2×#67766, #10704972, … |
| maximal normal subgroup of | D3×#1335, C2×#67766, #10704972, … |
| maximal quotient of | #10681836, #10681839, #10681854, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 342);