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)(12,15,17,24)(13,19,20,27)(14,21,16,23)(18,26,25,22);(12,14,17,16)(13,18,20,25)(15,23,24,21)(19,22,27,26);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,18)(15,22)(16,25)(17,20)(19,21)(23,27)(24,26)Polycyclic presentation:
2^6,7|a^2=d,b^2=f,c^2=f,e^2=f,c^a=ce,e^a=ef,g^a=g^6,c^b=cf,e^c=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11727427, #11727447, #11727860, … |
| maximal normal subgroup of | #11727427, #11727447, #11727860, … |
| maximal quotient of | #11729307, #11729312, #11729375, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 759);