Finite Group Databasebeta

C4×#65229 #12020458

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct productC4×#65229

Splittings

FittingC2×C43×C5 ⋊ C2
SylowC5 ⋊ C4×#388

Subgroups

subgroupG/H
centerC23×C4C22×D5
commutatorC22×C5C22×C42
FrattiniC24C23×D5
FittingC2×C43×C5C2
socle, cosocleC24×C5C24
prime radicalC24×D5C23
hypercenterC2×C43D5
hypocenterC5C4×#388
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C4 ◁ C2×C43

2134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 640

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 90726);