Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C26 |
| direct product | C22×D53⋊C32 |
| unambiguous semidirect product | D53⋊(C22×C32) |
| derived, Sylow | C53 ⋊ C23×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | #6157 |
| commutator, hypocenter | C53 | C23×C32 |
| Frattini | C8 | C23×#6157 |
| Fitting | C22×C16×C53 | C4 |
| socle | C23×C53 | C2×C16 |
| prime radical | C23×D53 | C16 |
| cosocle | #11719908 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C16 | |
542 conjugacy classes of subgroups; only the 320 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 320 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 6784 |
1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114079);