Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #447 |
198 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 112 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11)(12,13,17,19,15,18,14,16);(8,9)(10,11);(2,3)(4,5)(6,7)(13,16)(14,17)(18,19)Polycyclic presentation:
2^6,7|c^2=df,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725860, #11725861, #11725884, … |
| maximal normal subgroup of | #11725860, #11725861, #11725884, … |
| maximal quotient of | #11725860, #11725864, #11725885, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 266);