Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #361 |
62 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)(9,13)(10,18)(11,21)(14,15)(16,23)(17,20)(19,22);(2,3)(4,5)(6,7)(8,9,10,14,12,17,18,16)(11,20,19,15,22,13,21,23)Polycyclic presentation:
2^6,7|a^2=c,c^2=f,d^2=e,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,c^b=cf,d^b=def,e^b=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#361, #11727010, #11727011, … |
| maximal normal subgroup of | D7×#361, #11727010, #11727011, … |
| maximal quotient of | #11725529, #11725568, #11725581, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 120);