Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #462 |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,7,5,3)(8,9)(10,11)(12,14,16,22)(13,17,19,20)(15,24,23,21)(18,27,26,25);(8,9,10,11)(14,21)(15,23)(17,25)(18,26)(20,27)(22,24);(2,3)(4,5)(6,7)(8,9,10,11)(12,13,16,19)(14,20,22,17)(15,18,23,26)(21,27,24,25)Polycyclic presentation:
2^6,7|a^2=e,b^2=ef,c^2=f,d^2=f,c^a=ce,g^a=g^6,c^b=cd,d^b=df,d^c=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11736251, #11736255, #11736260, … |
| maximal normal subgroup of | #11736251, #11736255, #11736260, … |
| maximal quotient of | #11726220, #11726221, #11726228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 327);