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C4×D8×AGL(1,𝔽5) #13033784

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D8×AGL(1,𝔽5)

Splittings

FittingC4×C5×D8 ⋊ C4
SylowC5 ⋊ C42×D8

Subgroups

subgroupG/H
centerC2×C4D4×AGL(1,𝔽5)
commutatorC4×C5C22×C42
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC4×C5×D8C4
socleC22×C5C2×C4×D4
prime radicalC2×D5×D8C22
cosocleC2×C4×D5C24
hypercenterC4×D8AGL(1,𝔽5)
hypocenterC5C42×D8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

1350 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#2177, AGL(1,𝔽5)×#1580, AGL(1,𝔽5)×#1333, …
maximal normal subgroup ofAGL(1,𝔽5)×#2177, AGL(1,𝔽5)×#1580, AGL(1,𝔽5)×#1333, …
maximal quotient ofAGL(1,𝔽5)×#2177, AGL(1,𝔽5)×#2179, C4×D8×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1104052);