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C2×D5⋊#324 #13029176

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×D5⋊#324
unambiguous semidirect productD5⋊(C2×#324)

Splittings

SylowC5 ⋊ C22×#324

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C23×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC24×D5C2×C4
cosocleC22×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C22×#324
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

1806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1099444);