Finite Group Databasebeta

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C22×AGL(1,𝔽5)×#127 #72221486

order2560
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214×C4

Aliases

direct productC22×AGL(1,𝔽5)×#127

Splittings

FittingC22×C5×#127 ⋊ C4
SylowC5 ⋊ C22×C4×#127

Subgroups

subgroupG/H
centerC24C23×AGL(1,𝔽5)
commutatorC22×C5C25×C4
FrattiniC22C25×AGL(1,𝔽5)
FittingC22×C5×#127C4
socleC24×C5C23×C4
prime radicalC22×D5×#127C2
cosocleC22×D5C26
hypercenterC22×#127AGL(1,𝔽5)
hypocenterC5C22×C4×#127
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#127

46356 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.