Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ #518 |
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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 — 4 generators on 19 points:
(1,2,4,6,7,5,3)(8,9,10,11)(14,18)(16,19);(13,17)(16,19);(12,14)(13,16)(15,18)(17,19);(2,3)(4,5)(6,7)(12,13)(14,16)(15,17)(18,19)Polycyclic presentation:
2^6,7|d^2=e,c^a=cf,g^a=g^6,d^b=df94 conjugacy classes — view the full character table.
| maximal subgroup of | #11726714, #11726715, #11726716, … |
| maximal normal subgroup of | #11726714, #11726715, #11726716, … |
| maximal quotient of | #11730767, #11730778, #11730779, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 939);