Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C211×C42 |
| direct product | C22×#16811365 |
| Fitting | C22×#124×C53 ⋊ C2 |
| Sylow | C53 ⋊ C22×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D53 |
| commutator, cosocle | C22×C53 | C26 |
| Frattini | C22 | C25×D53 |
| Fitting | C22×#124×C53 | C2 |
| socle | C24×C53 | C24 |
| hypercenter | C22×#124 | D53 |
| hypocenter | C53 | C22×H(3,𝔽4) |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C24 ◁ C22×#124 | |
10246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1076440);