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C22×D5⋊#104 #13044487

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

Aliases

direct productC22×D5⋊#104
unambiguous semidirect productD5⋊(C22×#104)

Splittings

FittingC22×C5×#41 ⋊ C4
SylowC5 ⋊ C23×#104

Subgroups

subgroupG/H
centerC22×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×#41C4
socleC23×C5C2×C22⋊C4
prime radicalC22×D5×#41C2
cosocleC4×D5C25
hypercenterC22×#41AGL(1,𝔽5)
hypocenterC5C23×#104
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

5758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114755);