Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C7×SD16 ⋊ C2 |
| Sylow | C7 ⋊ #468 |
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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) = 224 |
A minimal faithful permutation representation — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11)(13,17)(14,18)(16,19);(12,13,14,17,15,16,18,19);(2,3)(4,5)(6,7)(8,9)(10,11)(13,16)(17,19)Polycyclic presentation:
2^6,7|b^2=e,e^2=f,b^a=bf,c^a=cd,g^a=g^6,c^b=cef,e^c=ef58 conjugacy classes — view the full character table.
| maximal subgroup of | #11737109, #11737110, #11737113, … |
| maximal normal subgroup of | #11737109, #11737110, #11737113, … |
| maximal quotient of | #11727929, #11727934, #11727942, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 708);