Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C7 ⋊ #385 |
234 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 91 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)(13,15)(16,17,18,19);(12,13)(14,15);(2,3)(4,5)(6,7)(8,9,10,11)(17,19)Polycyclic presentation:
2^6,7|a^2=d,c^2=e,c^a=ce,g^a=g^6,c^b=cf88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726712, #11726715, #11727775, … |
| maximal normal subgroup of | #11726712, #11726715, #11727775, … |
| maximal quotient of | #11727161, #11727166, #11727173, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 484);