Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C7 ⋊ #364 |
46 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)(8,10,11,18,13,19,17,22,14,20,16,23,12,21,9,15);(2,3)(4,5)(6,7)(8,9,12,16,14,17,13,11)(10,18,19,22,20,23,21,15)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,c^2=e,d^2=f,e^2=f,b^a=bd,g^a=g^6,d^b=df88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726842, #11726843, #11726868, … |
| maximal normal subgroup of | #11726842, #11726843, #11726868, … |
| maximal quotient of | #11725360, #11725361, #11725616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 68);