Finite Group Databasebeta

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C3×C7×Dic5×C13⋊C3 #30655209

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

Aliases

direct productC3×C7×Dic5×C13⋊C3
unambiguous semidirect product(C13×Dic5)⋊(C32×C7)
unambiguous semidirect product(C3×C13×Dic5)⋊(C3×C7)

Splittings

derived, HallC5×C13 ⋊ C32×C4×C7
HallC3×C5×C7×C13⋊C3 ⋊ C4
HallC7×C13×Dic5 ⋊ C32
HallC3×C5×C13⋊C3 ⋊ C4×C7
HallC5×C7×C13 ⋊ C32×C4
HallC13×Dic5 ⋊ C32×C7
HallC7×C13 ⋊ C32×Dic5
HallC5×C7 ⋊ C3×C4×C13⋊C3
SylowC13 ⋊ C32×C7×Dic5
SylowC5 ⋊ C3×C4×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D5×C13⋊C3
commutator, hypocenterC5×C13C32×C4×C7
FrattiniC2C3×C7×D5×C13⋊C3
Fitting, socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C5×C7×C13⋊C3C2
cosocleC2×C5×C13C2×C32×C7
LCSG ▷ C5×C13
UCSC1 ◁ C2×C3×C7

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5460

Conjugacy classes & character table

1176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 259);