Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
| direct product | C32×#88324 |
| derived, Sylow | C53 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | #6157 |
| commutator, hypocenter | C53 | C8×C32 |
| Frattini | C2×C16 | C2×#6157 |
| Fitting | C2×C32×C53 | C4 |
| socle, prime radical | C22×C53 | C4×C16 |
| cosocle | C16×Dic53 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C32 | |
134 conjugacy classes of subgroups.
| 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, 1084329);