Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #1141 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C7 ⋊ Q8⋊C8 |
70 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)(8,9,10,12,11,13,14,15)(17,20)(18,23)(21,22);(2,3)(4,5)(6,7)(16,17,19,22)(18,20,23,21)Polycyclic presentation:
2^6,7|a^2=f,b^2=c,c^2=e,d^2=f,b^a=bd,d^a=df,g^a=g^6,d^b=df88 conjugacy classes — view the full character table.
| maximal subgroup of | #11725919, #11725920, #11725923, … |
| maximal normal subgroup of | #11725919, #11725920, #11725923, … |
| maximal quotient of | #11725283, #11725286, #11725364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 41);