Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4466 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C3 ⋊ #1398 |
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)(5,10,12,14)(6,15)(11,24,25,22)(13,23,27,28)(16,29)(17,21)(26,34,35,33)(30,32);(1,2,3)(4,5,6,11,7,13,16,26,8,14,17,24,18,28,30,34,9,12,15,25,19,27,29,35,20,10,21,22,31,23,32,33)Polycyclic presentation:
2^7,3|a^2=c,b^2=d,c^2=e,e^2=f,f^2=g,b^a=bf,d^a=dg,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#1398, C2×#67600, #10715373, … |
| maximal normal subgroup of | D3×#1398, C2×#67600, #10715373, … |
| maximal quotient of | #10682516, #10682521, #10682875, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 176);