Finite Group Databasebeta

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C4⋊C4×#683 #12020737

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4⋊C4×#683

Splittings

SylowC5 ⋊ C4⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC2×C4×C5×C4⋊C4C2
socle, prime radical, cosocleC24×C5C24
hypercenterC2×C4×C4⋊C4D5
hypocenterC5C4⋊C42
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

1838 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1280

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, 91005);