Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3243 |
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:
(1,2,3)(5,11)(9,12)(10,19)(17,18)(22,29)(25,33)(30,35)(32,34);(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(21,26)(23,31)(25,32)(27,28)(30,35)(33,34);(2,3)(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17)(20,22,24,29)(21,25,28,33)(23,30,31,35)(26,32,27,34);(4,5)(6,12)(7,10)(8,11)(9,14)(13,18)(15,17)(16,19)(20,21)(22,25)(23,26)(24,28)(27,31)(29,33)(30,32)(34,35)Polycyclic presentation:
2^7,3|b^2=eg,c^2=e,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ce,d^b=dg,h^b=h^2,f^c=fg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3243, C2×#81279, #11667432, … |
| maximal normal subgroup of | D3×#3243, C2×#81279, #11667432, … |
| maximal quotient of | #10804734, #10804951, #10805780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 13855);