Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #2103 |
148 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 3 generators on 35 points:
(2,3)(4,7,8,22,9,23,10,24)(5,12,13,29,14,20,25,34)(6,16,17,31,19,32,18,21)(11,26,15,28,27,35,30,33);(1,2,3)(4,6,10,17,9,19,8,18)(5,11,25,15,14,27,13,30)(7,21,24,16,23,31,22,32)(12,28,34,35,20,33,29,26);(4,5,8,13,9,14,10,25)(6,15,17,27,19,30,18,11)(7,20,22,34,23,12,24,29)(16,28,31,35,32,33,21,26)Polycyclic presentation:
2^7,3|a^2=d,b^2=de,c^2=d,d^2=g,f^2=g,b^a=bd,c^a=ce,f^a=fg,c^b=cf,d^b=dg,e^b=eg,f^b=fg,h^c=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | #10708544, #10708549, #10708554, … |
| maximal normal subgroup of | #10708544, #10708549, #10708554, … |
| maximal quotient of | #10700311, #10700316, #10700321, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3302);