Finite Group Databasebeta

← Prev (#30655176) Next (#30655178) →

C2×C9×C13×D35 #30655177

order16380
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C13×D35
unambiguous semidirect product(C2×C5)⋊(C9×C13×D7)

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, HallC5×C7 ⋊ C22×C9×C13
HallC5×C7×C9×C13 ⋊ C22
HallC7×C9×C13 ⋊ C2×D5
HallC5×C9×C13 ⋊ C2×D7
HallC5×C7×C13 ⋊ C22×C9
HallC5×C7×C9 ⋊ C22×C13
HallC7×C13 ⋊ C2×C9×D5
HallC5×C13 ⋊ C2×C9×D7
HallC7×C9 ⋊ C2×D5×C13
HallC5×C9 ⋊ C2×C13×D7
SylowC7 ⋊ C2×C9×D5×C13
SylowC5 ⋊ C2×C9×C13×D7

Subgroups

subgroupG/H
center, hypercenterC2×C9×C13D35
commutator, hypocenterC5×C7C22×C9×C13
FrattiniC3C2×C3×C13×D35
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C13×D35C3
cosocleC3×C5×C7C22×C3×C13
LCSG ▷ C5×C7
UCSC1 ◁ C2×C9×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

4446 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 227);