Finite Group Databasebeta

← Prev (#19150043) Next (#19150045) →

C2×C5⋊(D31⋊C9) #19150044

order5580
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5⋊(D31⋊C9)
unambiguous semidirect product(C2×C5)⋊(D31⋊C9)
unambiguous semidirect product(C2×C31⋊C9)⋊D5
unambiguous semidirect product(C2×D155)⋊C9

Splittings

derived, HallC5×C31 ⋊ C22×C9
HallC5×C31⋊C9 ⋊ C22
HallC2×D155 ⋊ C9
HallC31⋊C9 ⋊ C2×D5
SylowC31 ⋊ C2×C9×D5
SylowC5 ⋊ C2×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D31⋊C3)
commutator, hypocenterC5×C31C22×C9
FrattiniC3C2×C5⋊(D31⋊C3)
Fitting, socleC2×C3×C5×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C2×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

222 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C25⋊(D31⋊C9), C2×C5⋊((D31⋊C5)⋊C9), D5×C5⋊(D31⋊C9), …
maximal normal subgroup ofC2×C5⋊((D31⋊C5)⋊C9), C2×C5×C5⋊(D31⋊C9)
maximal quotient ofC2×C25⋊(D31⋊C9), D5×C5⋊(D31⋊C9), C2×C5×C5⋊(D31⋊C9), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 33);