Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C3 ⋊ #1407 |
98 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)(4,6,9,17)(5,10,13,26)(7,15,19,33)(8,22,23,16)(11,27,28,14)(12,24,21,25)(18,30,34,29)(20,31,35,32);(2,3)(4,5)(6,14,16,29)(7,18,19,34)(8,21,23,12)(9,13)(10,15,24,31)(11,20)(17,27,22,30)(25,32,26,33)(28,35)Polycyclic presentation:
2^7,3|a^2=d,b^2=g,c^2=f,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,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×#1407, C2×#67549, #10715472, … |
| maximal normal subgroup of | D3×#1407, C2×#67549, #10715472, … |
| maximal quotient of | #10682567, #10682607, #10682698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 125);