Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #491 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 31 points:
(1,2,4,6,7,5,3)(8,10,11,15)(9,13,12,14)(17,22)(18,24)(19,27)(21,28)(25,26)(29,31);(9,12)(13,14)(16,18,20,26)(17,21,22,29)(19,24,27,25)(23,31,30,28);(2,3)(4,5)(6,7)(8,9,11,12)(10,14,15,13)(16,17)(18,21)(19,23)(20,22)(24,31)(25,28)(26,29)(27,30)Polycyclic presentation:
2^6,7|a^2=e,b^2=f,c^2=e,d^2=f,b^a=be,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df58 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89569, #11736230, #11736255, … |
| maximal normal subgroup of | C2×#89569, #11736230, #11736255, … |
| maximal quotient of | #11726559, #11726564, #11726596, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 331);