Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #356 |
60 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)(8,10,13,11)(9,14,17,22)(12,20,21,19)(15,23,18,16);(2,3)(4,5)(6,7)(8,9,11,15,13,17,10,18)(12,16,19,22,21,23,20,14)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,c^2=f,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df55 conjugacy classes — view the full character table.
| maximal subgroup of | #11725269, #11725357, #11725358, … |
| maximal normal subgroup of | #11725269, #11725357, #11725358, … |
| maximal quotient of | #11725441, #11725449, #11725450, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 105);