Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #501 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,12,13,14)(16,17)(18,22)(19,20)(21,23);(8,9,11,13)(10,14,15,12)(17,20)(21,22);(2,3)(4,5)(6,7)(16,17,18,21,19,20,23,22)Polycyclic presentation:
2^6,7|a^2=e,b^2=d,c^2=d,e^2=f,b^a=bf,c^a=ce,g^a=g^6,c^b=cdf,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11726126, #11726127, #11726130, … |
| maximal normal subgroup of | #11726126, #11726127, #11726130, … |
| maximal quotient of | #11727295, #11727304, #11727309, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 599);