Finite Group Databasebeta

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Dic3×#3955 #14295437

order1920
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productDic3×#3955

Splittings

HallC3×C5 ⋊ C4×#100
SylowC5 ⋊ Dic3×#100
SylowC3 ⋊ C4×#3955

Subgroups

subgroupG/H
centerC22D3×#685
commutatorC22×C3×C5C2×C42
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D20C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5C4×#100
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

720 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 480

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21135);