Finite Group Databasebeta

← Prev (#30655168) Next (#30655170) →

C5×C13×C22⋊(C7⋊C9) #30655169

order16380
isoclinismisoclinic class of C22⋊ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C5×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C13×C22⋊(C7⋊C9)
unambiguous semidirect productC22⋊(C5×C13×C7⋊C9)
unambiguous semidirect productC7⋊(C5×C13×C22⋊C9)
unambiguous semidirect product(C22×C5)⋊(C13×C7⋊C9)
unambiguous semidirect product(C5×C7)⋊(C13×C22⋊C9)

Splittings

derived, HallC22×C7 ⋊ C5×C9×C13
HallC22×C5×C7×C13 ⋊ C9
HallC5×C7×C13 ⋊ C22⋊C9
HallC22×C7×C13 ⋊ C5×C9
HallC22×C5×C13 ⋊ C7⋊C9
HallC22×C5×C7 ⋊ C9×C13
HallC7×C13 ⋊ C5×C22⋊C9
HallC22×C13 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C13×C22⋊C9
HallC22×C5 ⋊ C13×C7⋊C9
SylowC7 ⋊ C5×C13×C22⋊C9
SylowC22 ⋊ C5×C13×C7⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13C22⋊ΓL(1,𝔽8)
commutator, hypocenterC22×C7C5×C9×C13
FrattiniC3C5×C13×C22⋊ΓL(1,𝔽8)
Fitting, socle, prime radicalC22×C3×C5×C7×C13C3
cosocleC22×C3×C7C3×C5×C13
LCSG ▷ C22×C7
UCSC1 ◁ C3×C5×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

2340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 219);