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C2×C4⋊C4×#170 #13033498

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

Aliases

direct productC2×C4⋊C4×#170

Splittings

SylowC5 ⋊ C2×C8×C4⋊C4

Subgroups

subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socle, prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×C8×C4⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C4⋊C4

1438 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 1103766);