Finite Group Databasebeta

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C2×C3×D2685 #44567397

order32220
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D2685
unambiguous semidirect product(C2×C3)⋊(C3×D895)
unambiguous semidirect product(C2×C5)⋊(C3×D537)
unambiguous semidirect product(C2×C179)⋊(C3×D15)

Splittings

Fitting, socleC2×C32×C5×C179 ⋊ C2
derivedC3×C5×C179 ⋊ C22×C3
HallC32×C5×C179 ⋊ C22
HallC32×C179 ⋊ C2×D5
HallC5×C179 ⋊ C2×C3×D3
SylowC179 ⋊ C2×C3×D15
HallC32×C5 ⋊ C2×D179
SylowC32 ⋊ C2×D895
SylowC5 ⋊ C2×C3×D537

Subgroups

subgroupG/H
center, hypercenterC2×C3D2685
commutator, cosocle, hypocenterC3×C5×C179C22×C3
FrattiniC1G
Fitting, socleC2×C32×C5×C179C2
LCSG ▷ C3×C5×C179
UCSC1 ◁ C2×C3

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10740

Conjugacy classes & character table

8064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32220, 84);