Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C32×#6157 |
| Fitting | C2×C32×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C2×C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #6157 |
| commutator, hypocenter | C53 | C2×C4×C32 |
| Frattini | C16 | C22×#6157 |
| Fitting | C2×C32×C53 | C4 |
| socle | C22×C53 | C4×C16 |
| prime radical | C22×D53 | C2×C16 |
| cosocle | C16×D53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C32 | |
270 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| 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, 1097781);