Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C7×C22⋊Q8 ⋊ C2 |
| Sylow | C7 ⋊ #452 |
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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) = 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)(12,15,17,23)(13,19,20,27)(14,21,16,25)(18,26,24,22);(8,9)(10,11)(12,14,17,16)(13,18,20,24)(15,21,23,25)(19,26,27,22);(2,3)(4,5)(6,7)(12,13)(14,18)(15,22)(16,24)(17,20)(19,21)(23,26)(25,27)Polycyclic presentation:
2^6,7|b^2=f,c^2=f,d^2=f,c^a=cd,d^a=df,g^a=g^6,c^b=ce,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11737587, #11737588, #11737593, … |
| maximal normal subgroup of | #11737587, #11737588, #11737593, … |
| maximal quotient of | #11727260, #11727276, #11727277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 581);