Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C22⋊C8 ⋊ C2 |
| Sylow | C7 ⋊ #408 |
158 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 55 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)(12,14,15,20,16,21,22,26)(13,18,19,25,17,23,24,27);(8,9)(10,11)(13,17)(18,23)(19,24)(25,27);(2,3)(4,5)(6,7)(12,13)(14,18)(15,19)(16,17)(20,25)(21,23)(22,24)(26,27)Polycyclic presentation:
2^6,7|c^2=d,d^2=f,b^a=bf,g^a=g^6,c^b=ce88 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89499, #11736045, #11736049, … |
| maximal normal subgroup of | C2×#89499, #11736045, #11736049, … |
| maximal quotient of | #11725858, #11725859, #11725876, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 261);