Finite Group Databasebeta

C22⋊C4×C22⋊Dic5 #12020702

order1280
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22⋊C4×C22⋊Dic5

Splittings

SylowC5 ⋊ C22⋊C42

Subgroups

subgroupG/H
center, FrattiniC24C23×D5
commutatorC22×C5C22×C42
FittingC23×C5×C22⋊C4C2
socle, cosocleC24×C5C24
prime radicalC26×C5C22
hypercenterC23×C22⋊C4D5
hypocenterC5C22⋊C42
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C22⋊C4

4254 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

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, 90970);