Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #467 |
114 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);(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22)Polycyclic presentation:
2^6,7|a^2=f,b^2=ef,e^2=f,b^a=be,c^a=cd,e^a=ef,g^a=g^6118 conjugacy classes — view the full character table.
| maximal subgroup of | #11725292, #11725294, #11725334, … |
| maximal normal subgroup of | #11725292, #11725294, #11725334, … |
| maximal quotient of | #11727521, #11727524, #11727529, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 650);