Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4487 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1369 |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 35 points:
(2,3)(4,6,7,18,9,20,24,19,11,22,25,33,10,21,8,26)(5,12,13,17,15,28,23,32,16,29,14,30,27,35,31,34);(1,2,3)(4,5,8,14,10,15,25,31,11,16,24,13,9,27,7,23)(6,17,19,28,21,32,18,29,22,30,26,35,20,34,33,12)Polycyclic presentation:
2^7,3|a^2=d,b^2=c,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,d^b=dg,h^b=h^260 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1369, C2×#67567, #10706750, … |
| maximal normal subgroup of | D3×#1369, C2×#67567, #10706750, … |
| maximal quotient of | #10681924, #10682072, C2×#67567, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 143);