Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C16 · Schur multiplier (H2) = C43 |
| direct product | C4×#16811509 |
| derived, Sylow | C53 ⋊ C42×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4×C8 | #6157 |
| commutator, hypocenter | C53 | C42×C16 |
| Frattini | C22×C4 | C22×#6157 |
| Fitting | C2×C4×C8×C53 | C4 |
| socle, prime radical | C23×C53 | C22×C8 |
| cosocle | C22×#88322 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C4×C8 | |
558 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 360 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 13568 |
1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1095660);