Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#107 ⋊ C2 |
| Sylow | C7 ⋊ #428 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(13,17)(14,19)(16,18);(12,13,14,18,15,16,19,17);(2,3)(4,5)(6,7)(13,16)(17,18)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,e^2=f,b^a=bf,g^a=g^6,c^b=ce,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89653, #11736591, #11736603, … |
| maximal normal subgroup of | C2×#89653, #11736591, #11736603, … |
| maximal quotient of | #11726322, #11726325, #11726328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 415);