Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3237 |
322 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)(20,23,25,24)(21,27,28,32)(22,31,30,33)(26,35,34,29);(4,7,8,16)(5,10,11,19)(6,13,14,15)(9,17,12,18)(20,22)(21,26)(23,31)(24,33)(25,30)(27,35)(28,34)(29,32);(2,3)(4,6,8,14)(5,9,11,12)(7,15,16,13)(10,18,19,17)(22,30)(26,34)(29,35)(31,33);(4,5)(6,12)(7,10)(8,11)(9,14)(13,18)(15,17)(16,19)(20,21,25,28)(22,29,30,35)(23,27,24,32)(26,33,34,31)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,d^a=de,f^a=fg,c^b=ceg,h^b=h^2,f^c=fg45 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3237, C2×#81502, #11667358, … |
| maximal normal subgroup of | D3×#3237, C2×#81502, #11667358, … |
| maximal quotient of | #10804707, #10804944, #10805754, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14078);