Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C137 · Schur multiplier (H2) = C29 |
| direct product | C22×#41×C137 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C137 | C22 |
| commutator, Frattini, cosocle | C2 | C25×C137 |
| socle | C23×C137 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C137 ◁ G | |
890 conjugacy classes of subgroups.
5480 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 263);