Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C7 ⋊ #495 |
130 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(9,11)(13,18)(14,21)(15,24)(17,25)(20,27)(22,23);(9,11)(12,14)(13,17)(15,21)(16,23)(18,20)(19,27)(22,24)(25,26);(2,3)(4,5)(6,7)(8,9,10,11)(12,13)(14,20)(15,19)(16,18)(17,23)(21,25)(22,27)(24,26)Polycyclic presentation:
2^6,7|a^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 | #11726938, #11726939, #11726957, … |
| maximal normal subgroup of | #11726938, #11726939, #11726957, … |
| maximal quotient of | #11727912, #11727935, #11727943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 689);