Finite Group DatabasebetaFinite Group Databasebeta| order | 448 |
| isoclinism | isoclinic class of #90632 |
| automorphism | ? |
| homology | Abelianization (H1) = C7 · Schur multiplier (H2) = C23 |
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 | |
411 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 14 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2,4,6,8,10,12)(3,5,7,9,11,13,14);(6,9)(12,14)Polycyclic presentation:
7,2^6|b^a=bd,c^a=bcd,d^a=bc,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, 1394);