Finite Group Databasebeta

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C22×#65729 #13044537

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#65729

Splittings

SylowC5 ⋊ C22×#430

Subgroups

subgroupG/H
centerC23C2×C4⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC22×C5×M16C4
socleC23×C5C2×C4⋊C4
prime radicalC24×D5Q8
cosocleC4×D5C25
hypercenterC22×M16AGL(1,𝔽5)
hypocenterC5C22×#430
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

2718 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 1114805);