Finite Group Databasebeta

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C2×C4×#4034 #12257820

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

Aliases

direct productC2×C4×#4034

Splittings

SylowC5 ⋊ C2×C4×C4⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socle, prime radicalC24×C5C24
cosocleC23×C5C25
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C2×C4×C4⋊Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C4×C4⋊C4

3358 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

Conjugacy classes & character table

272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 328088);