Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89246 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #333 |
64 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)(8,10,11,13,12,14,15,9)(17,21)(18,19)(22,23);(2,3)(4,5)(6,7)(8,9,11,14,12,13,15,10)(16,17,19,21,20,23,18,22)Polycyclic presentation:
2^6,7|a^2=d,b^2=cd,c^2=ef,d^2=f,b^a=bc,c^a=ce,g^a=g^6,c^b=cf,d^b=df79 conjugacy classes — view the full character table.
| maximal subgroup of | #11725937, #11725945, #11725952, … |
| maximal normal subgroup of | #11725937, #11725945, #11725952, … |
| maximal quotient of | #11725286, #11725379, #11725380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 38);