Finite Group Databasebeta

← Prev (#13031595) Next (#13031597) →

#137×#170 #13031596

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct product#137×#170

Splittings

SylowC5 ⋊ C8×#137

Subgroups

subgroupG/H
centerC22C2×D4×AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#137C4
socleC22×C5C2×C4×D4
prime radicalC2×C5×#41C2×C4
cosocleC4×Dic5C24
hypercenterC2×#137AGL(1,𝔽5)
hypocenterC5C8×#137
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1101864);