Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C64 · Schur multiplier (H2) = C23 |
| direct product | C2×D53⋊C64 |
| unambiguous semidirect product | D53⋊(C2×C64) |
| derived, Sylow | C53 ⋊ C22×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #6157 |
| commutator, hypocenter | C53 | C22×C64 |
| Frattini | C16 | C22×#6157 |
| Fitting | C2×C32×C53 | C4 |
| socle | C22×C53 | C2×C32 |
| prime radical | C22×D53 | C32 |
| cosocle | #13133123 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C32 | |
142 conjugacy classes of subgroups.
| 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, 1098145);