Finite Group Databasebeta

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C2×#11756516 #14509953

order1920
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#11756516

Splittings

FittingC22×C3×C5×D8 ⋊ C2
HallC3×C5 ⋊ C2×#576
SylowC5 ⋊ C2×#5757
SylowC3 ⋊ C2×#66091

Subgroups

subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC22×C3×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC22×D8D15
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D8

3024 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

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, 235651);