Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C53×#564 ⋊ C4 |
| Sylow | C53 ⋊ #34526 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×#6157 |
| commutator, socle | C22×C53 | C24×C4 |
| Fitting | C53×#564 | C4 |
| prime radical, cosocle | C22×D53 | C25 |
| hypercenter | #564 | #6157 |
| hypocenter | C53 | #34526 |
| LCS | G ▷ C22×C53 ▷ C53 | |
| UCS | C1 ◁ C22 ◁ #564 | |
1800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3392 |
Polycyclic presentation:
2^8,53|a^2=h,b^2=fg,c^2=fgh,d^2=f,e^2=h,b^a=bf,c^a=cg,d^a=dg,e^a=ef,i^a=i^23,c^b=cg,d^b=df,i^c=i^23,i^e=i^30,i^h=i^52323 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1114637);