Finite Group Databasebeta

C42×D4×D5 #12257488

order1280
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C29×C4

Aliases

direct productC42×D4×D5

Splittings

FittingC42×C5×D4 ⋊ C2
SylowC5 ⋊ C2×C42×D4

Subgroups

subgroupG/H
centerC2×C42C22×D5
commutatorC2×C5C23×C42
FrattiniC23C24×D5
FittingC42×C5×D4C2
socle, cosocleC23×C5C25
prime radicalC22×D4×D5C22
hypercenterC42×D4D5
hypocenterC5C2×C42×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C42 ◁ C42×D4

5694 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 327756);