Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89261 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ H(3,ℤ/4) |
94 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)(8,10)(9,13,14,20)(11,18)(12,17)(15,16,21,22)(19,23);(2,3)(4,5)(6,7)(8,9)(10,16,17,22)(11,15)(12,14)(13,18,20,23)(19,21)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,e^2=f,b^a=be,d^a=df,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11726451, #11726453, D7×H(3,ℤ/4), … |
| maximal normal subgroup of | #11726451, #11726453, D7×H(3,ℤ/4), … |
| maximal quotient of | #11725420, #11725422, #11725427, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 88);