Finite Group DatabasebetaFinite Group Databasebeta| order | 12608 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C197 · Schur multiplier (H2) = C25 |
| direct product | C2×C4⋊Q8×C197 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C197 | C23 |
| commutator, Frattini, cosocle | C22 | C24×C197 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C197 ◁ G | |
290 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12608 |
5516 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12608, 212);