Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #353 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C137 · Schur multiplier (H2) = C2 |
| direct product | #356×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C137 | #99 |
| commutator | C2×C4 | C2×C4×C137 |
| Frattini, cosocle | C2×Q8 | C22×C137 |
| prime radical | C22×C137 | C22⋊C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C137 ◁ C22×C137 ◁ C2×Q8×C137 ◁ G | |
60 conjugacy classes of subgroups.
1781 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 37);