Finite Group Databasebeta

← Prev (#14514179) Next (#14514181) →

C4×A4×C22⋊D5 #14514180

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24

Aliases

direct productC4×A4×C22⋊D5
unambiguous semidirect product(C22×C4×C22⋊D5)⋊C3

Splittings

FittingC24×C4×C5 ⋊ C2×C3
HallC22×C4×C22⋊D5 ⋊ C3
SylowC5 ⋊ C4×D4×A4

Subgroups

subgroupG/H
centerC2×C4C2×D5×A4
commutatorC23×C5C22×C3×C4
FrattiniC22C22×D5×A4
FittingC24×C4×C5C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC2×A4×C22⋊D5C2
hypercenterC22×C4D5×A4
hypocenterC22×C5C3×C4×D4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

208 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 239878);