Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #3374 |
326 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 384 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2)(4,6,7,11)(5,9,8,10);(12,14,16,21)(13,17,19,26)(15,24,25,22)(18,27,23,20);(4,5,7,8)(6,10,11,9)(14,21)(17,26)(20,27)(22,24);(2,3)(5,8)(9,10)(12,13,16,19)(14,20,21,27)(15,23,25,18)(17,24,26,22)Polycyclic presentation:
2^7,3|a^2=g,b^2=e,c^2=g,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^2,c^b=cg,d^b=de,f^c=fg,h^d=h^251 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#3374, C2×#79817, #11674998, … |
| maximal normal subgroup of | D3×#3374, C2×#79817, #11674998, … |
| maximal quotient of | #10811835, #10812046, #10814165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 12393);