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C8×D4×AGL(1,𝔽5) #13033716

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C25×C4

Aliases

direct productC8×D4×AGL(1,𝔽5)

Splittings

FittingC5×C8×D4 ⋊ C4
SylowC5 ⋊ C4×C8×D4

Subgroups

subgroupG/H
centerC2×C8C22×AGL(1,𝔽5)
commutatorC2×C5C22×C4×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC5×C8×D4C4
socleC22×C5C22×C42
prime radicalC2×D4×D5C2×C4
cosocleC2×C4×D5C24
hypercenterC8×D4AGL(1,𝔽5)
hypocenterC5C4×C8×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C8×D4

1422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽5)×#1580, C8×D4×#1043, AGL(1,𝔽5)×#2970, …
maximal normal subgroup ofAGL(1,𝔽5)×#1580, AGL(1,𝔽5)×#2970, AGL(1,𝔽5)×#2968
maximal quotient ofAGL(1,𝔽5)×#1580, AGL(1,𝔽5)×#2171, C8×D4×#1043

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1103984);