Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #324 |
78 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(16,18,19,23)(17,20,21,22);(2,3)(4,5)(6,7)(8,9,10,12,11,13,14,15)(16,17)(18,22,23,20)(19,21)Polycyclic presentation:
2^6,7|a^2=c,b^2=f,c^2=e,b^a=bd,d^a=df,g^a=g^6,c^b=cf82 conjugacy classes — view the full character table.
| maximal subgroup of | #11725258, #11725259, #11725260, … |
| maximal normal subgroup of | #11725258, #11725259, #11725260, … |
| maximal quotient of | #11725419, #11725438, #11725441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 85);