Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #90631 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C26 ⋊ C7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C26 | C7 |
| LCS | G ▷ C26 | |
| UCS | C1 | |
424 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 28 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3,4,6,8,5,7)(10,11,12,14,16,13,15);(9,13)(10,11)(12,16)(14,15);(1,5)(2,3)(4,8)(6,7)Polycyclic presentation:
7,2^6|b^a=c,c^a=d,d^a=bd,e^a=f,f^a=g,g^a=eg16 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(448, 1393);