Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #474 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,12,13,14)(17,20)(18,23)(21,22);(8,9,11,13)(10,14,15,12);(2,3)(4,5)(6,7)(16,17)(18,20)(19,22)(21,23)Polycyclic presentation:
2^6,7|b^2=e,c^2=e,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11726194, #11726195, #11726198, … |
| maximal normal subgroup of | #11726194, #11726195, #11726198, … |
| maximal quotient of | #11727321, #11727325, #11727338, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 621);