Finite Group Databasebeta

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C2×D3×#3992 #14411215

order1920
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26

Aliases

direct productC2×D3×#3992

Splittings

FittingC2×C3×C5×C8 ⋊ C2×C4
HallC3×C5 ⋊ C22×#97
SylowC5 ⋊ C2×D3×#97
SylowC3 ⋊ C22×#3992

Subgroups

subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C22×C42
FrattiniC4C22×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C42
prime radicalC22×D3×D5C2×C4
cosocleC3×C4×D5C24
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5C22×#97
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 240

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×AGL(1,𝔽5)×#97
maximal normal subgroup ofD3×AGL(1,𝔽5)×#97

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 136913);