Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #323 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,12,11,13,14,15)(16,18)(17,20,21,22)(19,23);(2,3)(4,5)(6,7)(16,17)(18,22)(19,21)(20,23)Polycyclic presentation:
2^6,7|b^2=c,c^2=e,b^a=bd,c^a=cf,g^a=g^6,d^b=df82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725855, #11725857, #11725858, … |
| maximal normal subgroup of | #11725855, #11725857, #11725858, … |
| maximal quotient of | #11725250, #11725251, #11725260, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 25);