Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#20288949 |
| Fitting | C2×C53×#560 ⋊ C2 |
| Sylow | C53 ⋊ C2×#3537 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D53 |
| commutator, cosocle | C22×C53 | C26 |
| Frattini | C22 | C25×D53 |
| Fitting | C2×C53×#560 | C2 |
| socle | C23×C53 | C25 |
| hypercenter | C2×#560 | D53 |
| hypocenter | C53 | C2×#3537 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C23 ◁ C2×#560 | |
8890 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
1064 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1076800);