Finite Group Databasebeta

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C22×AGL(1,𝔽5)×#97 #72242646

order2560
automorphism?
homologyAbelianization (H1) = C22×C43 · Schur multiplier (H2) = C28×C42

Aliases

direct productC22×AGL(1,𝔽5)×#97

Splittings

FittingC22×C5×#97 ⋊ C4
SylowC5 ⋊ C22×C4×#97

Subgroups

subgroupG/H
centerC23×C4C22×AGL(1,𝔽5)
commutatorC2×C5C22×C43
FrattiniC2×C4C24×AGL(1,𝔽5)
FittingC22×C5×#97C4
socleC24×C5C2×C42
prime radicalC24×D5C22×C4
cosocleC2×C4×D5C25
hypercenterC22×#97AGL(1,𝔽5)
hypocenterC5C22×C4×#97
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C22×#97

11460 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC22×#72220669
maximal quotient ofC22×#72220669

GAP

Past the SmallGroups library coverage — no SmallGroups id.