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C2×C4×D5×AGL(1,𝔽5) #13107611

order1600
isoclinismisoclinic class of D5×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×D5×AGL(1,𝔽5)
unambiguous semidirect productD5⋊(C42×D5)

Splittings

FittingC2×C4×C52 ⋊ C2×C4
derived, SylowC52 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC2×C4D5×AGL(1,𝔽5)
commutator, hypocenterC52C22×C42
FrattiniC2C22×D5×AGL(1,𝔽5)
FittingC2×C4×C52C2×C4
socleC22×C52C22×C4
prime radicalC22×D52C22
cosocleC2×C5×D5C24
LCSG ▷ C52
UCSC1 ◁ C2×C4

1023 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C4×AGL(1,𝔽5)2, C2×D5×#87830, C2×D4×D5×AGL(1,𝔽5), …
maximal normal subgroup ofC2×C4×AGL(1,𝔽5)2, C2×D4×D5×AGL(1,𝔽5), C2×AGL(1,𝔽5)×C4⋊AGL(1,𝔽5)
maximal quotient ofC2×D5×#87830, C2×AGL(1,𝔽5)×#6036

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9963);