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C5×D5⋊#131 #13107730

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×D5⋊#131
unambiguous semidirect productD5⋊(C5×#131)

Splittings

SylowC52 ⋊ C2×#131

Subgroups

subgroupG/H
centerC4×C5C22×AGL(1,𝔽5)
commutatorC2×C5C23×C4×C5
FrattiniC2C23×C5×AGL(1,𝔽5)
FittingC52×#41C4
socleC2×C52C23×C4
prime radicalC5×D5×#41C2
cosocleDic5C24×C5
hypercenterC5×#41AGL(1,𝔽5)
hypocenterC5C2×C5×#131
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C4×C5 ◁ C5×#41

552 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 10082);