Finite Group Databasebeta

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C2×#11748339 #14414855

order1920
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#11748339

Splittings

HallC3×C5 ⋊ C2×#436
SylowC5 ⋊ C2×#5012
SylowC3 ⋊ C2×#65018

Subgroups

subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C22×C4
prime radicalC22×C3×C22⋊D5C4
cosocleC2×C3×C4×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#436
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

1104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 960

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 140553);