Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Fitting | C7×#125 ⋊ C2 |
| Sylow | C7 ⋊ #488 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,13,12,14)(17,22)(19,27)(21,28)(23,24)(25,31)(29,30);(8,9,11,12)(10,14,15,13)(16,18,20,26)(17,21,24,30)(19,25,27,31)(22,28,23,29);(2,3)(4,5)(6,7)(9,12)(13,14)(16,17)(18,21)(19,22)(20,24)(23,27)(25,28)(26,30)(29,31)Polycyclic presentation:
2^6,7|b^2=ef,c^2=e,d^2=f,b^a=be,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | #11738595, #11738596, #11738631, … |
| maximal normal subgroup of | #11738595, #11738596, #11738631, … |
| maximal quotient of | #11727301, #11727305, #11727311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 602);