Finite Group Databasebeta

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C2×C3⋊D3045 #49141695

order36540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D3045
unambiguous semidirect product(C2×C3)⋊D3045
unambiguous semidirect product(C2×C5)⋊(C3⋊D609)
unambiguous semidirect product(C2×C7)⋊(C3⋊D435)
unambiguous semidirect product(C2×C29)⋊(C3⋊D105)

Splittings

Fitting, socleC2×C32×C5×C7×C29 ⋊ C2
derived, HallC32×C5×C7×C29 ⋊ C22
HallC32×C7×C29 ⋊ C2×D5
HallC32×C5×C29 ⋊ C2×D7
HallC5×C7×C29 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D29
HallC32×C29 ⋊ C2×D35
HallC7×C29 ⋊ C2×C3⋊D15
HallC5×C29 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×D145
HallC32×C5 ⋊ C2×D203
HallC5×C7 ⋊ C2×C3⋊D87
SylowC29 ⋊ C2×C3⋊D105
SylowC32 ⋊ C2×D1015
SylowC7 ⋊ C2×C3⋊D435
SylowC5 ⋊ C2×C3⋊D609

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D3045
commutator, cosocle, hypocenterC32×C5×C7×C29C22
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C29C2
LCSG ▷ C32×C5×C7×C29
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18270

Conjugacy classes & character table

9138 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36540, 537);