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A4×#4027 #14513987

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

Aliases

direct productA4×#4027
unambiguous semidirect product(C22×#4027)⋊C3

Splittings

FittingC22×C5×C22⋊C4 ⋊ C2×C3
HallC22×#4027 ⋊ C3
SylowC5 ⋊ C4×D4×A4

Subgroups

subgroupG/H
center, FrattiniC22C22×D5×A4
commutatorC23×C5C22×C3×C4
FittingC22×C5×C22⋊C4C2×C3
socle, cosocleC24×C5C23×C3
prime radicalC2×A4×C22⋊D5C2
hypercenterC22⋊C4D5×A4
hypocenterC22×C5C3×C4×D4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C22⋊C4

1156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

160 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 239685);