Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C7×#107 ⋊ C2 |
| Sylow | C7 ⋊ #357 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(8,9,10,11)(13,17)(14,21)(15,22)(18,19)(20,26)(23,27)(24,25);(2,3)(4,5)(6,7)(12,13)(14,17)(15,24)(16,20)(18,21)(19,22)(23,26)(25,27)Polycyclic presentation:
2^6,7|b^2=c,d^2=ef,e^2=f,b^a=bd,d^a=de,e^a=ef,g^a=g^6,d^b=de,e^b=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11726937, #11726940, D7×#357, … |
| maximal normal subgroup of | #11726937, #11726940, D7×#357, … |
| maximal quotient of | #11725277, #11725279, #11725281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 48);