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D9×D31⋊C25 #42124274

order27900
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productD9×D31⋊C25
unambiguous semidirect productD31⋊(D9×C25)
unambiguous semidirect product(D9×D31)⋊C25
unambiguous semidirect product(C9×D31⋊C25)⋊C2
unambiguous semidirect product(D9×C31⋊C25)⋊C2
unambiguous semidirect product(C9⋊(D31⋊C25))⋊C2

Splittings

derived, HallC9×C31 ⋊ C22×C25
HallC9×C31⋊C25 ⋊ C22
HallD9×D31 ⋊ C25
HallC31⋊C25 ⋊ C2×D9
SylowC31 ⋊ C2×D9×C25
SylowC9 ⋊ C2×D31⋊C25

Subgroups

subgroupG/H
center, hypercenterC5D9×D31⋊C5
commutator, hypocenterC9×C31C22×C25
FrattiniC3×C5D3×D31⋊C5
Fitting, cosocleC5×C9×C31C22×C5
socleC3×C5×C31C2×C5×D3
prime radicalC5×D9×D31C5
LCSG ▷ C9×C31
UCSC1 ◁ C5

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

390 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 21);