Finite Group DatabasebetaFinite Group Databasebeta| order | 7648 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C239 · Schur multiplier (H2) = C22 |
| direct product | #123×C239 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C239 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C239 |
| prime radical | C2×D4×C239 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C239 ◁ G | |
78 conjugacy classes of subgroups.
3346 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7648, 30);