Finite Group Databasebeta

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C22×AGL(1,𝔽5)×H(5,𝔽2) #72242755

order2560
automorphism?
homologyAbelianization (H1) = C26×C4 · Schur multiplier (H2) = C220

Aliases

direct productC22×AGL(1,𝔽5)×H(5,𝔽2)

Splittings

FittingC22×C5×H(5,𝔽2) ⋊ C4
SylowC5 ⋊ C22×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×AGL(1,𝔽5)
commutatorC2×C5C26×C4
FrattiniC2C26×AGL(1,𝔽5)
FittingC22×C5×H(5,𝔽2)C4
socleC23×C5C24×C4
prime radicalC22×D5×H(5,𝔽2)C2
cosocleC2×D5C27
hypercenterC22×H(5,𝔽2)AGL(1,𝔽5)
hypocenterC5C22×C4×H(5,𝔽2)
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

125924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

Relationships

maximal subgroup ofAGL(1,𝔽5)×#32898, AGL(1,𝔽5)×C22⋊#997, AGL(1,𝔽5)×#35346
maximal normal subgroup ofAGL(1,𝔽5)×#32898, AGL(1,𝔽5)×C22⋊#997, AGL(1,𝔽5)×#35346
maximal quotient ofAGL(1,𝔽5)×#62817

GAP

Past the SmallGroups library coverage — no SmallGroups id.