Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 6 |
| isoclinism | isoclinic class of D64 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C31 · Schur multiplier (H2) = C2 |
| direct product | C31×#7539 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C31 | D32 |
| commutator | C32 | C2×C4×C31 |
| Frattini, cosocle | C2×C32 | C22×C31 |
| socle | C2×C31 | #1415 |
| prime radical | C31×#2262 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C31 ◁ C2×C4×C31 ◁ C2×C8×C31 ◁ C2×C16×C31 ◁ C2×C31×C32 ◁ G | |
88 conjugacy classes of subgroups.
2170 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 527);