Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#501 ⋊ C2 |
| Sylow | C3 ⋊ #3244 |
320 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2)(5,11)(9,12)(10,19)(17,18)(21,27)(22,30)(26,28)(31,35);(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(21,26)(22,30)(24,32)(25,33)(27,28)(29,34);(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17)(20,22)(21,25)(23,30)(24,31)(26,34)(27,29)(28,33)(32,35);(2,3)(4,5)(6,12)(7,10)(8,11)(9,14)(13,18)(15,17)(16,19)(20,21)(22,29)(23,27)(24,26)(25,30)(28,32)(31,33)(34,35)Polycyclic presentation:
2^7,3|b^2=eg,c^2=eg,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,h^a=h^2,c^b=ce,d^b=dg,f^c=fg,h^d=h^242 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3244, C2×#81989, #11667437, … |
| maximal normal subgroup of | D3×#3244, C2×#81989, #11667437, … |
| maximal quotient of | #10804733, #10804965, #10805774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14565);