Finite Group Databasebeta

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C3×C7×#63121⋊C3 #30655323

order16380
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×#63121⋊C3
unambiguous semidirect product#63121⋊(C32×C7)
unambiguous semidirect product(C3×#63121)⋊(C3×C7)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C3×C4
derived, HallC5×C13 ⋊ C32×C4×C7
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC7×#63121 ⋊ C32
HallC3×C7×C13⋊C3 ⋊ AGL(1,𝔽5)
HallC3×C5×C13⋊C3 ⋊ C4×C7
HallC5×C7×C13 ⋊ C32×C4
Hall#63121 ⋊ C32×C7
HallC3×C13⋊C3 ⋊ C7×AGL(1,𝔽5)
HallC7×C13 ⋊ C32×AGL(1,𝔽5)
HallC5×C7 ⋊ C3×AGL(1,𝔽13)
SylowC13 ⋊ C32×C7×AGL(1,𝔽5)
SylowC5 ⋊ C3×C7×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC3×C7#63121⋊C3
commutator, hypocenterC5×C13C32×C4×C7
FrattiniC1G
Fitting, socleC3×C5×C7×C13C3×C4
prime radicalC3×C7×C5⋊(D13⋊C3)C2
cosocleD65C2×C32×C7
LCSG ▷ C5×C13
UCSC1 ◁ C3×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1365

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 373);