Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C7×#107 ⋊ C2 |
| Sylow | C7 ⋊ #427 |
114 conjugacy classes of subgroups.
| 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)(8,9,10,11)(13,18)(14,20)(15,23)(17,24)(21,22)(25,27);(12,14,15,21,16,22,23,20)(13,17,19,24,18,25,26,27);(2,3)(4,5)(6,7)(12,13)(14,17)(15,19)(16,18)(20,27)(21,24)(22,25)(23,26)Polycyclic presentation:
2^6,7|b^2=e,c^2=d,e^2=f,c^a=cf,g^a=g^6,c^b=ce,e^c=ef70 conjugacy classes — view the full character table.
| maximal subgroup of | #11726936, #11726942, #11726944, … |
| maximal normal subgroup of | #11726936, #11726942, #11726944, … |
| maximal quotient of | #11726321, #11726324, #11726327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 414);