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C13×C3⋊Dic105 #30655281

order16380
automorphism?
homologyAbelianization (H1) = C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC13×C3⋊Dic105
unambiguous semidirect productC3⋊(C13×Dic105)
unambiguous semidirect productC7⋊(C13×C3⋊Dic15)

Splittings

derived, HallC32×C5×C7 ⋊ C4×C13
HallC32×C5×C7×C13 ⋊ C4
HallC32×C7×C13 ⋊ Dic5
HallC32×C5×C13 ⋊ Dic7
HallC5×C7×C13 ⋊ C3⋊Dic3
HallC32×C13 ⋊ Dic35
HallC7×C13 ⋊ C3⋊Dic15
HallC5×C13 ⋊ C3⋊Dic21
HallC32×C7 ⋊ C13×Dic5
HallC32×C5 ⋊ C13×Dic7
HallC5×C7 ⋊ C13×C3⋊Dic3
SylowC32 ⋊ C13×Dic35
SylowC7 ⋊ C13×C3⋊Dic15
SylowC5 ⋊ C13×C3⋊Dic21

Subgroups

subgroupG/H
center, hypercenterC2×C13C3⋊D105
commutator, hypocenterC32×C5×C7C4×C13
FrattiniC2C13×C3⋊D105
Fitting, socle, prime radicalC2×C32×C5×C7×C13C2
cosocleC2×C32×C5×C7C2×C13
LCSG ▷ C32×C5×C7
UCSC1 ◁ C2×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16380

Conjugacy classes & character table

4134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 331);