Finite Group Databasebeta

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#41×D5⋊C8 #13044834

order1280
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct product#41×D5⋊C8
unambiguous semidirect productD5⋊(C8×#41)

Splittings

SylowC5 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC42C22×AGL(1,𝔽5)
commutatorC2×C5C24×C8
FrattiniC22C24×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C24×C4
prime radicalC2×D5×#41C4
cosocleC2×Dic5C25
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C2×C8×#41
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C4×#41

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1115102);