Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×D8 ⋊ C2 |
| Sylow | C7 ⋊ #509 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(9,15)(10,12)(11,19)(14,16)(17,23)(18,20)(21,22);(8,10,13,12)(9,14,17,21)(11,18,20,19)(15,22,23,16);(2,3)(4,5)(6,7)(8,9)(10,14)(11,15)(12,21)(13,17)(16,19)(18,22)(20,23)Polycyclic presentation:
2^6,7|b^2=f,d^2=ef,e^2=f,c^a=cd,d^a=de,e^a=ef,g^a=g^6,c^b=cf,d^c=de,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11727008, #11727016, #11727017, … |
| maximal normal subgroup of | #11727008, #11727016, #11727017, … |
| maximal quotient of | #11728350, #11728352, #11728354, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 681);