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#41×C22⋊AGL(1,𝔽5) #13043945

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct product#41×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×#41 ⋊ C4
SylowC5 ⋊ C22⋊C4×#41

Subgroups

subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutator, socleC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC22×C5×#41C4
prime radicalC22×D5×#41C2
cosocleC22×D5C25
hypercenterC22×#41AGL(1,𝔽5)
hypocenterC5C22⋊C4×#41
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C22×#41

5646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114213);