Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×C7×D4 ⋊ C2 |
| Sylow | C7 ⋊ #447 |
198 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 198 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 — 3 generators on 19 points:
(1,2,4,6,7,5,3)(9,11);(13,16)(14,19)(17,18);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,16)(15,18)(17,19)Polycyclic presentation:
2^6,7|e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6,e^b=ef79 conjugacy classes — view the full character table.
| maximal subgroup of | #11727450, #11727451, #11727456, … |
| maximal normal subgroup of | #11727450, #11727451, #11727456, … |
| maximal quotient of | #11729309, #11729314, #11729360, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 751);