Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #470 |
110 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)(14,22)(17,26)(20,27)(23,25);(12,14,21,25,16,22,15,23)(13,17,24,27,19,26,18,20);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,16,19)(14,20,22,27)(15,24,21,18)(17,25,26,23)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^6,c^b=cf76 conjugacy classes — view the full character table.
| maximal subgroup of | #11725288, #11725290, #11725342, … |
| maximal normal subgroup of | #11725288, #11725290, #11725342, … |
| maximal quotient of | #11727571, #11727574, #11727578, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 671);