Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #498 |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,12,13,14)(17,20)(18,22)(21,23);(16,17,18,20,19,21,22,23);(2,3)(4,5)(6,7)(8,9,11,13)(10,14,15,12)Polycyclic presentation:
2^6,7|a^2=d,b^2=e,c^2=d,e^2=f,c^a=cd,g^a=g^6,c^b=cef,e^c=ef64 conjugacy classes — view the full character table.
| maximal subgroup of | #11727000, #11727069, C2×#89627, … |
| maximal normal subgroup of | #11727000, #11727069, C2×#89627, … |
| maximal quotient of | #11726557, #11726581, #11726589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 389);