Finite Group DatabasebetaFinite Group Databasebeta| order | 1960 |
| isoclinism | isoclinic class of AGL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C72 · Schur multiplier (H2) = C7 |
| Fitting, socle | C23×C5×C7 ⋊ C7 |
| derived, Sylow | C23 ⋊ C5×C72 |
| Hall | C23×C5 ⋊ C72 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | AGL(1,𝔽8) |
| commutator, cosocle, hypocenter | C23 | C5×C72 |
| Frattini | C1 | G |
| Fitting, socle | C23×C5×C7 | C7 |
| LCS | G ▷ C23 | |
| UCS | C1 ◁ C5×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 280 |
280 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1960, 127);