Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C32 · Schur multiplier (H2) = C8 |
No aliases for this group.
| derived, Sylow | C53 ⋊ C8×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4×C16 | #6157 |
| commutator, hypocenter | C53 | C8×C32 |
| Frattini | C4×C8 | C2×#6157 |
| Fitting | C4×C16×C53 | C4 |
| socle, prime radical | C22×C53 | C4×C16 |
| cosocle | C4×#11719908 | C22 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C4×C16 | |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13568 |
Polycyclic presentation:
2^8,53|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,i^a=i^30,i^b=i^52,i^c=i^521088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1084331);