Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #353 |
86 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 56 |
A minimal faithful permutation representation — 2 generators on 15 points:
(1,2,4,6,7,5,3)(9,12)(10,15)(13,14);(2,3)(4,5)(6,7)(8,9)(10,13,15,12)(11,14)Polycyclic presentation:
2^6,7|a^2=c,d^2=f,b^a=bd,d^a=def,e^a=ef,g^a=g^6,c^b=ce,d^b=df,d^c=df55 conjugacy classes — view the full character table.
| maximal subgroup of | #11725268, #11725345, #11725346, … |
| maximal normal subgroup of | #11725268, #11725345, #11725346, … |
| maximal quotient of | #11725441, #11725446, #11725447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 102);