Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1132 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C7 ⋊ #341 |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,4,6,7,5,3)(8,9,10,11)(12,14,15,22,17,24,16,23)(13,18,25,27,20,26,19,21);(2,3)(4,5)(6,7)(12,13,15,19,17,20,16,25)(14,21,22,26,24,27,23,18)Polycyclic presentation:
2^6,7|a^2=c,b^2=de,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^6124 conjugacy classes — view the full character table.
| maximal subgroup of | #11725333, #11725335, #11725581, … |
| maximal normal subgroup of | #11725333, #11725335, #11725581, … |
| maximal quotient of | #11725460, #11725462, #11725485, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 109);