Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #6400 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #358 |
58 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
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)(12,13,16,20)(14,17,23,26)(15,24,22,19)(18,27,25,21)Polycyclic presentation:
2^6,7|a^2=f,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 | #11726938, #11726939, #11726942, … |
| maximal normal subgroup of | #11726938, #11726939, #11726942, … |
| maximal quotient of | #11725278, #11725280, #11725282, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 49);