Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
No aliases for this group.
| Fitting | C4×H(5,𝔽2)×C53 ⋊ C2 |
| Sylow | C53 ⋊ #62847 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C25×D53 |
| commutator, socle, cosocle | C22×C53 | C26 |
| Fitting | C4×H(5,𝔽2)×C53 | C2 |
| hypercenter | C4×H(5,𝔽2) | D53 |
| hypocenter | C53 | #62847 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ C4×H(5,𝔽2) | |
7106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|b^2=g,e^2=g,b^a=bg,c^a=ch,f^a=fh,e^b=eh,i^b=i^52,d^c=dh1850 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1078626);