Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #89332 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ #329 |
70 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,4,6,7,5,3)(9,12)(10,14)(16,17)(18,22)(19,21)(20,23);(2,3)(4,5)(6,7)(8,9,10,13,11,12,14,15)(17,20,21,22)Polycyclic presentation:
2^6,7|a^2=c,c^2=ef,d^2=f,b^a=bd,d^a=def,g^a=g^6,c^b=ce,d^b=df61 conjugacy classes — view the full character table.
| maximal subgroup of | #11725348, #11725352, #11725577, … |
| maximal normal subgroup of | #11725348, #11725352, #11725577, … |
| maximal quotient of | #11725436, #11725445, #11725448, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 97);