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C4×#64891 #13025682

order1280
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#64891

Splittings

SylowC5 ⋊ C4×#349

Subgroups

subgroupG/H
centerC42C22⋊AGL(1,𝔽5)
commutatorC22×C5C2×C4×C8
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC2×C4×C5×C8C4
socleC22×C5C2×C22⋊C8
prime radicalC23×D5C2×C8
cosocleC22×#168C23
hypercenterC2×C4×C8AGL(1,𝔽5)
hypocenterC5C4×#349
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8

522 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1095950);