Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #342 |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(12,14)(13,16)(15,19)(17,18);(2,3)(4,5)(6,7)(12,13)(14,18,19,16)(15,17)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,b^a=be,e^a=ef,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725254, #11725255, #11725256, … |
| maximal normal subgroup of | #11725254, #11725255, #11725256, … |
| maximal quotient of | #11725419, #11725422, C7⋊#1304, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 83);