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C4×D5⋊#100 #13033358

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D5⋊#100

Splittings

SylowC5 ⋊ C2×C4×#100

Subgroups

subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC22×C5C22×C22⋊C4
prime radicalC22×D4×D5C22
cosocleC22×Dic5C24
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C2×C4×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×D4

1970 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

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, 1103626);