Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67573 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1366 |
74 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2)(4,6,9,16)(5,10)(7,19,22,24)(8,23,20,18)(11,15)(12,28)(13,32)(14,26)(17,21,33,31)(25,29)(27,34)(30,35);(2,3)(4,5,7,12,20,13,31,29,9,14,22,30,8,11,21,27)(6,15,17,28,23,26,19,34,16,32,33,35,18,10,24,25)Polycyclic presentation:
2^7,3|a^2=d,b^2=f,c^2=fg,d^2=ef,e^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=def,e^b=eg,h^b=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1366, C2×#67574, #10706553, … |
| maximal normal subgroup of | D3×#1366, C2×#67574, #10706553, … |
| maximal quotient of | #10682012, #10682366, C2×#67574, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 150);