Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #62636 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C31 · Schur multiplier (H2) = C29 |
| direct product | C31×#62637 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C31 | C23×D8 |
| commutator, Frattini, cosocle | C8 | C25×C31 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C31 ◁ C2×#41×C31 ◁ C2×C31×#131 ◁ G | |
2026 conjugacy classes of subgroups.
1798 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 55625);