Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| 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)(12,14,15,23,17,24,16,25)(13,18,19,26,21,27,20,22);(2,3)(4,5)(6,7)(8,9,10,11)(12,13,16,20,17,21,15,19)(14,22,23,18,24,26,25,27)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,c^2=f,d^2=f,b^a=bde,g^a=g^6,d^b=df88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726454, #11726472, #11726492, … |
| maximal normal subgroup of | #11726454, #11726472, #11726492, … |
| maximal quotient of | #11725468, #11725473, #11725475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 115);