Finite Group Databasebeta

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C4×#65845 #12259266

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#65845

Splittings

FittingC2×C4×C5×C4⋊C4 ⋊ C2
SylowC5 ⋊ C4×#554

Subgroups

subgroupG/H
centerC22×C4C23×D5
commutatorC22×C5C24×C4
FrattiniC23C24×D5
FittingC2×C4×C5×C4⋊C4C2
socle, cosocleC23×C5C25
prime radicalC22×C22⋊D5C23
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4×#554
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

2516 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 329534);