Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C263 · Schur multiplier (H2) = C25 |
| direct product | 2−1+4×C263 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C263 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C263 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C263 ◁ G | |
146 conjugacy classes of subgroups.
4471 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 50);