Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #1413 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(1,2,3)(4,6,9,16)(5,10)(7,19,21,25)(8,22,24,18)(11,15)(12,29)(13,32)(14,27)(17,20,34,23)(26,28)(30,35)(31,33);(2,3)(4,5,7,12,9,14,21,31)(6,15,17,33,16,32,34,29)(8,13,23,30,24,11,20,28)(10,25,26,18,27,19,35,22)Polycyclic presentation:
2^7,3|a^2=d,b^2=f,c^2=fg,d^2=g,e^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,c^b=cf,d^b=def,e^b=eg,d^c=dfg,e^d=eg30 conjugacy classes — view the full character table.
| maximal subgroup of | #10683033, #10683034, #10683036, … |
| maximal normal subgroup of | #10683033, #10683034, #10683036, … |
| maximal quotient of | #10682578, #10682596, #10682727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 362);