Finite Group Databasebeta

C2×C7×C9×D5×C13 #30655175

order16380
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C7×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C9×D5×C13
unambiguous semidirect productC5⋊(C22×C7×C9×C13)
unambiguous semidirect product(C2×C5)⋊(C2×C7×C9×C13)

Splittings

FittingC2×C5×C7×C9×C13 ⋊ C2
derived, SylowC5 ⋊ C22×C7×C9×C13
HallC5×C7×C9×C13 ⋊ C22
HallC5×C9×C13 ⋊ C22×C7
HallC5×C7×C13 ⋊ C22×C9
HallC5×C7×C9 ⋊ C22×C13
HallC5×C13 ⋊ C22×C7×C9
HallC5×C9 ⋊ C22×C7×C13
HallC5×C7 ⋊ C22×C9×C13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C9×C13D5
commutator, hypocenterC5C22×C7×C9×C13
FrattiniC3C2×C3×C7×D5×C13
FittingC2×C5×C7×C9×C13C2
socleC2×C3×C5×C7×C13C2×C3
prime radicalC2×C3×C7×D5×C13C3
cosocleC3×C5C22×C3×C7×C13
LCSG ▷ C5
UCSC1 ◁ C2×C7×C9×C13

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 225);