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C2×C5×D4×AGL(1,𝔽5) #13107724

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26

Aliases

direct productC2×C5×D4×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C4×C5×D4)

Splittings

FittingC2×C52×D4 ⋊ C4
SylowC52 ⋊ C2×C4×D4

Subgroups

subgroupG/H
centerC22×C5C22×AGL(1,𝔽5)
commutatorC2×C5C23×C4×C5
FrattiniC2C23×C5×AGL(1,𝔽5)
FittingC2×C52×D4C4
socleC22×C52C22×C4
prime radicalC2×C5×D4×D5C2
cosocleC2×D5C24×C5
hypercenterC2×C5×D4AGL(1,𝔽5)
hypocenterC5C2×C4×C5×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

879 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽5)×#127, C5×AGL(1,𝔽5)×#120, C2×D4×AGL(1,ℤ/25), …
maximal normal subgroup ofC5×AGL(1,𝔽5)×#127, C5×AGL(1,𝔽5)×#120, C2×D4×D5×AGL(1,𝔽5), …
maximal quotient ofC5×AGL(1,𝔽5)×#127, C5×AGL(1,𝔽5)×#120, C2×D4×AGL(1,ℤ/25), …
automorphism group ofC11×Dic10, C11×D20, C2×C11×Dic5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 10076);