Finite Group Databasebeta

← Prev (#42124381) Next (#42124383) →

C2×C3×(D31⋊C3)⋊C25 #42124382

order27900
automorphism?
homologyAbelianization (H1) = C22×C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3×(D31⋊C3)⋊C25
unambiguous semidirect product(D31⋊C3)⋊(C2×C3×C25)
unambiguous semidirect product(C2×D31⋊C3)⋊(C3×C25)
unambiguous semidirect product(C2×C3×D31⋊C3)⋊C25
unambiguous semidirect product(D31⋊C25)⋊(C2×C32)
unambiguous semidirect product((C31⋊C3)⋊C25)⋊(C22×C3)
unambiguous semidirect product(C2×D31⋊C25)⋊C32
unambiguous semidirect product(C2×(C31⋊C3)⋊C25)⋊(C2×C3)
unambiguous semidirect product(C2×C3×D31⋊C25)⋊C3

Splittings

derived, SylowC31 ⋊ C22×C32×C25
HallC3×(C31⋊C3)⋊C25 ⋊ C22
HallC2×D31⋊C25 ⋊ C32
HallC2×C3×D31⋊C3 ⋊ C25
HallC31⋊C25 ⋊ C22×C32
HallC3×C31⋊C3 ⋊ C22×C25
HallC2×D31 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5AGL(1,𝔽31)
commutator, hypocenterC31C22×C32×C25
FrattiniC5C2×C3×AGL(1,𝔽31)
Fitting, socleC2×C3×C5×C31C2×C3×C5
prime radicalC2×C3×C5×D31⋊C3C5
cosocleC5×C31C22×C32×C5
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

930 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 129);