Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(7,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C4×C53 · Schur multiplier (H2) = C214 |
| direct product | C53×#62652 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C53 | C26 |
| commutator | C2 | C25×C4×C53 |
| Frattini, cosocle | C22 | C26×C53 |
| prime radical | C22×H(5,𝔽2)×C53 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C53 ◁ G | |
11674 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
6890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 55640);