Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C7 ⋊ #488 |
96 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 224 |
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)(18,25)(19,28)(21,29)(24,31)(26,27);(9,12)(13,14)(16,18)(17,21)(19,25)(20,27)(22,24)(23,31)(26,28)(29,30);(2,3)(4,5)(6,7)(8,9,11,12)(10,14,15,13)(16,17)(18,24)(19,23)(20,22)(21,27)(25,29)(26,31)(28,30)Polycyclic presentation:
2^6,7|a^2=e,c^2=e,d^2=f,b^a=bef,c^a=cef,g^a=g^6,c^b=cd,d^b=df,d^c=df64 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#89540, #11736182, #11736204, … |
| maximal normal subgroup of | C2×#89540, #11736182, #11736204, … |
| maximal quotient of | #11726558, #11726566, #11726599, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 302);