Finite Group DatabasebetaFinite Group Databasebeta| order | 7936 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 1238630400 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C210 |
| abelian | C24×C16×C31 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini | C8 | C25×C31 |
| socle | C25×C31 | C8 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
2590 conjugacy classes of subgroups.
7936 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C24×C31×C32, C23×C4×C16×C31, C25×C16×C31, … |
| maximal normal subgroup of | C24×C31×C32, C23×C4×C16×C31, C25×C16×C31, … |
| maximal quotient of | C24×C31×C32, C23×C4×C16×C31, C25×C16×C31, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7936, 55608);