Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C44 · Schur multiplier (H2) = C46 |
| direct product | C43×#6157 |
| Fitting | C43×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C44 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | #6157 |
| commutator, hypocenter | C53 | C44 |
| Frattini | C23 | C23×#6157 |
| Fitting | C43×C53 | C4 |
| socle | C23×C53 | C23×C4 |
| prime radical, cosocle | C23×D53 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C43 | |
3966 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1098151);