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C2×D5⋊#329 #13030701

order1280
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5⋊#329
unambiguous semidirect productD5⋊(C2×#329)

Splittings

SylowC5 ⋊ C22×#329

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#124C4
socleC23×C5C2×C22⋊C4
prime radicalC22×D4×D5C4
cosocleC4×Dic5C24
hypercenterC2×#124AGL(1,𝔽5)
hypocenterC5C22×#329
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#124

1502 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1100969);