Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C7×Q16 ⋊ C2 |
| Sylow | C7 ⋊ #451 |
148 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(12,14,16,22)(13,17,19,26)(15,24,25,21)(18,27,23,20);(12,13,16,19)(14,20,22,27)(15,23,25,18)(17,24,26,21);(2,3)(4,5)(6,7)(8,9)(10,11)Polycyclic presentation:
2^6,7|b^2=f,c^2=f,e^2=f,c^a=cd,g^a=g^6,c^b=ce,e^b=ef,e^c=ef61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737167, #11737168, #11737169, … |
| maximal normal subgroup of | #11737167, #11737168, #11737169, … |
| maximal quotient of | #11727985, #11727989, #11728020, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 720);