Finite Group Databasebeta

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C4×#65007 #12097422

order1280
automorphism?
homologyAbelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#65007

Splittings

SylowC5 ⋊ C4×#431

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC2×C5C22×C4×C8
FrattiniC22×C4C23×D5
FittingC4×C5×C22⋊C8C2
socleC23×C5C23×C4
prime radicalC24×C5C22×C4
cosocleC22×C4×C5C24
hypercenterC4×C22⋊C8D5
hypocenterC5C4×#431
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C4×C22⋊C8

1318 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 167690);