Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C7×#101 ⋊ C2 |
| Sylow | C7 ⋊ #355 |
64 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)(8,9,10,14,12,15,17,23)(11,13,19,20,18,21,16,22);(2,3)(4,5)(6,7)(9,13)(11,18)(14,22)(15,21)(16,19)(20,23)Polycyclic presentation:
2^6,7|b^2=c,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^6,d^b=def,e^b=ef,d^c=df46 conjugacy classes — view the full character table.
| maximal subgroup of | #11726914, #11726915, D7×#355, … |
| maximal normal subgroup of | #11726914, #11726915, D7×#355, … |
| maximal quotient of | #11725258, #11725260, #11725262, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 34);