Finite Group DatabasebetaFinite Group Databasebeta| order | 12608 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C197 · Schur multiplier (H2) = C210 |
| direct product | C23×D4×C197 |
| unambiguous semidirect product | C4⋊(C24×C197) |
| unambiguous semidirect product | C22⋊(C24×C197) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C197 | C22 |
| commutator, Frattini, cosocle | C2 | C25×C197 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C197 ◁ G | |
1362 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6304 |
7880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12608, 261);