Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #67579 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1426 |
52 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)(4,5,11,27,7,13,6,10,20,31,15,24,16,22,26,33,9,12,29,35,21,30,18,23,8,14,28,34,19,32,17,25);(2,3)(5,10,12,23)(6,15)(7,19)(8,20)(11,26)(13,27,30,35)(14,33,31,25)(16,21)(17,29)(18,28)(22,34,32,24)Polycyclic presentation:
2^7,3|a^2=d,b^2=cef,c^2=efg,e^2=fg,f^2=g,b^a=bc,c^a=ce,e^a=ef,f^a=fg,h^a=h^2,d^b=dg,h^b=h^248 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1426, C2×#67582, #10715706, … |
| maximal normal subgroup of | D3×#1426, C2×#67582, #10715706, … |
| maximal quotient of | #10682869, #10682896, C2×#67582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 158);