Finite Group Databasebeta

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C2×C3⋊D1365 #30655779

order16380
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D1365
unambiguous semidirect product(C2×C3)⋊D1365
unambiguous semidirect product(C2×C5)⋊(C3⋊D273)
unambiguous semidirect product(C2×C7)⋊(C3⋊D195)
unambiguous semidirect product(C2×C13)⋊(C3⋊D105)

Splittings

Fitting, socleC2×C32×C5×C7×C13 ⋊ C2
derived, HallC32×C5×C7×C13 ⋊ C22
HallC32×C7×C13 ⋊ C2×D5
HallC32×C5×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×C3⋊D3
HallC32×C5×C7 ⋊ C2×D13
HallC32×C13 ⋊ C2×D35
HallC7×C13 ⋊ C2×C3⋊D15
HallC5×C13 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×D65
HallC32×C5 ⋊ C2×D91
HallC5×C7 ⋊ C2×C3⋊D39
SylowC13 ⋊ C2×C3⋊D105
SylowC32 ⋊ C2×D455
SylowC7 ⋊ C2×C3⋊D195
SylowC5 ⋊ C2×C3⋊D273

Subgroups

subgroupG/H
center, hypercenterC2C3⋊D1365
commutator, cosocle, hypocenterC32×C5×C7×C13C22
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C13C2
LCSG ▷ C32×C5×C7×C13
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

4098 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 829);