Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C53 · Schur multiplier (H2) = C213 |
| direct product | C22×Q82×C53 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C53 | C24 |
| commutator, Frattini, cosocle | C22 | C26×C53 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C53 ◁ G | |
7846 conjugacy classes of subgroups; only the 6958 normal subgroups are shown.
This group has 7846 conjugacy classes of subgroups — too many to draw. Only its 6958 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13568 |
5300 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 55700);