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C4×D4×#170 #13033717

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D4×#170

Splittings

SylowC5 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC23×C5C23×C4
prime radicalC22×C5×D4C2×C4
cosocleC22×Dic5C24
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C4×C8×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103985);