Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#20289820 |
| derived, Sylow | C53 ⋊ C2×C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C16 | #6157 |
| commutator, hypocenter | C53 | C2×C4×C32 |
| Frattini | C2×C8 | C22×#6157 |
| Fitting | C22×C16×C53 | C4 |
| socle, prime radical | C23×C53 | C2×C16 |
| cosocle | C2×#11719908 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C16 | |
270 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 184 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, 1097784);