Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
| direct product | #564×#6157 |
| Fitting | C53×#564 ⋊ C4 |
| Sylow | C53 ⋊ C4×#564 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#6157 |
| commutator, socle | C22×C53 | C24×C4 |
| Fitting | C53×#564 | C4 |
| prime radical, cosocle | C22×D53 | C25 |
| hypercenter | #564 | #6157 |
| hypocenter | C53 | C4×#564 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1800 conjugacy classes of subgroups; only the 776 normal subgroups are shown.
This group has 1800 conjugacy classes of subgroups — too many to draw. Only its 776 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 3392 |
323 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114466);