Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| 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)(8,10,12,20,14,21,13,11)(9,15,17,19,18,16,22,23);(2,3)(4,5)(6,7)(8,9,11,16,13,17,21,23,14,18,20,15,12,22,10,19)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,c^2=e,d^2=f,e^2=f,b^a=bd,d^a=df,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725247, #11725249, #11725308, … |
| maximal normal subgroup of | #11725247, #11725249, #11725308, … |
| maximal quotient of | #11725245, #11725246, #11725464, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 20);