Finite Group Databasebeta

← Prev (#30655169) Next (#30655171) →

C5×C22⋊#11717941 #30655170

order16380
automorphism?
homologyAbelianization (H1) = C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C22⋊#11717941
unambiguous semidirect productC22⋊(C5×#11717941)
unambiguous semidirect product(C22×C5)⋊#11717941

Splittings

derived, HallC22×C7×C13 ⋊ C5×C9
HallC22×C5×C7×C13 ⋊ C9
HallC5×C7×C13 ⋊ C22⋊C9
HallC22×C5×C13 ⋊ C7⋊C9
HallC22×C5×C7 ⋊ C13⋊C9
HallC7×C13 ⋊ C5×C22⋊C9
HallC5×C13 ⋊ C22⋊(C7⋊C9)
HallC22×C13 ⋊ C5×C7⋊C9
HallC5×C7 ⋊ C22⋊(C13⋊C9)
HallC22×C7 ⋊ C5×C13⋊C9
HallC22×C5 ⋊ #11717941
SylowC13 ⋊ C5×C22⋊(C7⋊C9)
SylowC7 ⋊ C5×C22⋊(C13⋊C9)
SylowC22 ⋊ C5×#11717941

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊#63270
commutator, hypocenterC22×C7×C13C5×C9
FrattiniC3C5×C22⋊#63270
Fitting, socle, prime radicalC22×C3×C5×C7×C13C3
cosocleC22×C3×C7×C13C3×C5
LCSG ▷ C22×C7×C13
UCSC1 ◁ C3×C5

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8190

Conjugacy classes & character table

1860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16380, 220);