Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #419 |
150 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(8,10,11,9)(12,15,16,23,17,24,14,21)(13,19,18,22,20,27,25,26);(12,14,17,16)(13,18,20,25)(15,23,24,21)(19,26,27,22);(2,3)(4,5)(6,7)(8,9,11,10)(12,13)(14,18)(15,22)(16,25)(17,20)(19,23)(21,27)(24,26)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=de,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726466, #11726479, #11726513, … |
| maximal normal subgroup of | #11726466, #11726479, #11726513, … |
| maximal quotient of | #11727567, #11727576, #11727582, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 654);