Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C4⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #456 |
142 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)(8,11,13,10)(9,15,17,23)(12,18,22,20)(14,21,19,16);(8,10,13,11)(9,14,17,19)(12,20,22,18)(15,16,23,21);(2,3)(4,5)(6,7)(8,9)(10,14)(11,19)(12,21)(13,17)(15,20)(16,22)(18,23)Polycyclic presentation:
2^6,7|b^2=f,c^2=f,d^2=f,c^a=cd,d^a=df,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | #11725269, #11725356, #11726921, … |
| maximal normal subgroup of | #11725269, #11725356, #11726921, … |
| maximal quotient of | #11727327, #11727346, #11727347, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 629);