Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C16 · Schur multiplier (H2) = C25×C4 |
| direct product | C22×C16×#6157 |
| Fitting | C22×C16×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C22×C4×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | #6157 |
| commutator, hypocenter | C53 | C22×C4×C16 |
| Frattini | C8 | C23×#6157 |
| Fitting | C22×C16×C53 | C4 |
| socle | C23×C53 | C4×C8 |
| prime radical | C23×D53 | C2×C8 |
| cosocle | C8×D53 | C24 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C16 | |
1022 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, 1113357);