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C5×D5×AGL(1,ℤ/8) #13106926

order1600
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×D5×AGL(1,ℤ/8)

Splittings

FittingC52×AGL(1,ℤ/8) ⋊ C2
SylowC52 ⋊ C2×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C5C2×D4×D5
commutator, cosocleC4×C5C24×C5
FrattiniC4C23×C5×D5
FittingC52×AGL(1,ℤ/8)C2
socleC2×C52C22×D4
hypercenterC5×AGL(1,ℤ/8)D5
hypocenterC5C2×C5×AGL(1,ℤ/8)
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×AGL(1,ℤ/8)

664 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 80

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD52×AGL(1,ℤ/8), C5×#10619093, #72221384, …
maximal normal subgroup ofD52×AGL(1,ℤ/8), C5×#10619093, #72221384, …
maximal quotient ofAGL(1,ℤ/8)×D25⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9278);