Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C16 · Schur multiplier (H2) = C210 |
| direct product | C24×#11719910 |
| derived, Sylow | C53 ⋊ C24×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24×C4 | #6157 |
| commutator, hypocenter | C53 | C24×C16 |
| Frattini | C4 | C24×#6157 |
| Fitting | C24×C4×C53 | C4 |
| socle, prime radical | C25×C53 | C8 |
| cosocle | #88322 | C25 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C24×C4 | |
2590 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13568 |
1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1116259);