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C22×D5⋊#100 #13044458

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×D5⋊#100
unambiguous semidirect productD5⋊(C22×#100)

Splittings

SylowC5 ⋊ C23×#100

Subgroups

subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C24×C4
FrattiniC22C24×AGL(1,𝔽5)
FittingC23×C5×D4C4
socleC23×C5C2×C22⋊C4
prime radicalC23×D4×D5C2
cosocleC2×Dic5C25
hypercenterC23×D4AGL(1,𝔽5)
hypocenterC5C23×#100
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D4

7134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114726);