Finite Group Databasebeta

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C3×#10587935 #13132615

order1680
automorphism?
homologyAbelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#10587935

Splittings

HallC3×C5×C7 ⋊ M16
HallC5×C7 ⋊ C3×M16
HallC3×C7 ⋊ #704
HallC3×C5 ⋊ #1136
SylowC7 ⋊ C3×#704
SylowC5 ⋊ C3×#1136

Subgroups

subgroupG/H
centerC2×C3C2×C7⋊AGL(1,𝔽5)
commutatorC2×C5×C7C2×C3×C4
FrattiniC2C2×C3×C7⋊AGL(1,𝔽5)
Fitting, prime radicalC22×C3×C5×C7C4
socleC2×C3×C5×C7C2×C4
cosocleC7×Dic5C22×C3
hypercenterC22×C3C7⋊AGL(1,𝔽5)
hypocenterC5×C7C3×M16
LCSG ▷ C2×C5×C7 ▷ C5×C7
UCSC1 ◁ C2×C3 ◁ C22×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 840

Conjugacy classes & character table

186 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 635);