Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C22×C22⋊Q8×C53 ⋊ C2 |
| Sylow | C53 ⋊ #62819 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D53 |
| commutator, socle, cosocle | C22×C53 | C26 |
| Fitting | C22×C22⋊Q8×C53 | C2 |
| hypercenter | C22×C22⋊Q8 | D53 |
| hypocenter | C53 | #62819 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C22×C22⋊Q8 | |
7242 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1696 |
Polycyclic presentation:
2^8,53|b^2=g,c^2=g,b^a=bg,c^a=ch,d^a=dg,f^a=fh,i^a=i^52,c^b=cg,e^b=eh1532 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1078216);