Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C7 ⋊ #340 |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(12,13,14,15)(17,20)(18,23)(21,22);(2,3)(4,5)(6,7)(8,9,10,11)(16,17,18,21,19,22,23,20)Polycyclic presentation:
2^6,7|a^2=d,b^2=c,d^2=f,b^a=bde,g^a=g^6,d^b=df88 conjugacy classes — view the full character table.
| maximal subgroup of | #11726534, #11726535, #11726536, … |
| maximal normal subgroup of | #11726534, #11726535, #11726536, … |
| maximal quotient of | #11725418, #11725425, #11725426, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 86);