Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #449 |
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 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)(9,11)(12,15,14,13,17,19,16,18);(8,9)(10,11)(12,14,17,16)(13,15,18,19);(2,3)(4,5)(6,7)(12,13)(14,15)(16,19)(17,18)Polycyclic presentation:
2^6,7|b^2=f,c^2=df,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce79 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89506, #11736055, #11736058, … |
| maximal normal subgroup of | C2×#89506, #11736055, #11736058, … |
| maximal quotient of | #11725861, #11725865, #11725884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 268);