Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C16 · Schur multiplier (H2) = C210 |
| direct product | C23×D53⋊C16 |
| unambiguous semidirect product | D53⋊(C23×C16) |
| derived, Sylow | C53 ⋊ C24×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | #6157 |
| commutator, hypocenter | C53 | C24×C16 |
| Frattini | C4 | C24×#6157 |
| Fitting | C23×C8×C53 | C4 |
| socle | C24×C53 | C2×C8 |
| prime radical | C24×D53 | C8 |
| cosocle | #88322 | C25 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C8 | |
2590 conjugacy classes of subgroups; only the 1464 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 1464 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, 1116260);