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D4×C22⋊AGL(1,𝔽5) #10617508

order640
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×C22⋊AGL(1,𝔽5)

Splittings

FittingC22×C5×D4 ⋊ C4
SylowC5 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C23×AGL(1,𝔽5)
commutator, socleC22×C5C23×C4
FittingC22×C5×D4C4
prime radicalC22×D4×D5C2
cosocleC22×D5C24
hypercenterC22×D4AGL(1,𝔽5)
hypocenterC5D4×C22⋊C4
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13019964, #13019965, #13019972, …
maximal normal subgroup of#13019964, #13019965, #13019972, …
maximal quotient ofC22⋊C4×C22⋊AGL(1,𝔽5), C4⋊C4×C22⋊AGL(1,𝔽5), D4×(C2×AGL(1,𝔽5))⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(640, 19590);