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C2×D5×D5⋊C8 #13107596

order1600
isoclinismisoclinic class of D5×AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×D5×D5⋊C8
unambiguous semidirect productD5⋊(C2×C8×D5)

Splittings

derived, SylowC52 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4D5×AGL(1,𝔽5)
commutator, hypocenterC52C23×C8
FrattiniC2C22×D5×AGL(1,𝔽5)
FittingC2×C4×C52C2×C4
socleC22×C52C22×C4
prime radicalC22×D52C4
cosocleC5×Dic5C24
LCSG ▷ C52
UCSC1 ◁ C2×C4

703 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9948);