Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #342 |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 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) = 112 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,4,6,7,5,3)(12,14)(13,16,17,18)(15,19);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,18)(15,17)(16,19)Polycyclic presentation:
2^6,7|a^2=c,b^2=d,b^a=be,d^a=df,g^a=g^6,e^b=ef82 conjugacy classes — view the full character table.
| maximal subgroup of | C7⋊#2104, #11726705, #11726707, … |
| maximal normal subgroup of | C7⋊#2104, #11726705, #11726707, … |
| maximal quotient of | #11725418, #11725423, #11725424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 84);