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C22×D5×H(5,𝔽2) #13013185

order1280
automorphism?
homologyAbelianization (H1) = C27 · Schur multiplier (H2) = C220

Aliases

direct productC22×D5×H(5,𝔽2)

Splittings

FittingC22×C5×H(5,𝔽2) ⋊ C2
SylowC5 ⋊ C23×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×D5
commutator, cosocleC2×C5C27
FrattiniC2C26×D5
FittingC22×C5×H(5,𝔽2)C2
socleC23×C5C25
hypercenterC22×H(5,𝔽2)D5
hypocenterC5C23×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

65726 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD5×C22⋊#997, D5×#32898, C22×AGL(1,𝔽5)×H(5,𝔽2), …
maximal normal subgroup ofD5×C22⋊#997, D5×#32898, C22×AGL(1,𝔽5)×H(5,𝔽2), …
maximal quotient ofD5×#62817

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1083453);