Finite Group Databasebeta

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C2×#11746527 #14294476

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#11746527

Splittings

HallC3×C5 ⋊ C2×#339
SylowC5 ⋊ C2×#4523
SylowC3 ⋊ C2×#64900

Subgroups

subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#339
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

976 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 20174);