Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #431 |
118 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,9,10,12,11,13,14,15)(18,22)(20,23);(16,18)(17,20)(19,22)(21,23);(2,3)(4,5)(6,7)(16,17,19,21)(18,20,22,23)Polycyclic presentation:
2^6,7|a^2=e,c^2=d,d^2=f,g^a=g^6,c^b=ce100 conjugacy classes — view the full character table.
| maximal subgroup of | #11725854, #11725855, #11725858, … |
| maximal normal subgroup of | #11725854, #11725855, #11725858, … |
| maximal quotient of | #11726350, #11726356, #11726359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 252);