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C22×#64872 #13029665

order1280
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#64872

Splittings

SylowC5 ⋊ C22×Q8⋊C8

Subgroups

subgroupG/H
centerC24C22⋊AGL(1,𝔽5)
commutatorC4×C5C23×C8
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socle, prime radicalC24×C5C22⋊C4
cosocleC4×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C22×Q8⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

1454 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1099933);