Finite Group Databasebeta

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C2×C3×D1365 #30655787

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

Aliases

direct productC2×C3×D1365
unambiguous semidirect product(C2×C3)⋊(C3×D455)
unambiguous semidirect product(C2×C5)⋊(C3×D273)

Splittings

Fitting, socleC2×C32×C5×C7×C13 ⋊ C2
derivedC3×C5×C7×C13 ⋊ C22×C3
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, hypercenterC2×C3D1365
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C32×C5×C7×C13C2
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C2×C3

176 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

4104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 837);