Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #440 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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)(8,9,10,11)(12,14,15,16)(13,18,19,17);(13,17)(14,16)(18,19);(2,3)(4,5)(6,7)(12,13,15,19)(14,18,16,17)Polycyclic presentation:
2^6,7|a^2=f,c^2=d,e^2=f,b^a=be,e^a=ef,g^a=g^6,c^b=cf,e^b=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | #11737032, #11737034, #11737039, … |
| maximal normal subgroup of | #11737032, #11737034, #11737039, … |
| maximal quotient of | #11727213, #11727219, #11727229, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 552);