Finite Group Databasebeta

← Prev (#42124408) Next (#42124410) →

C2×C3⋊(C3⋊(D31⋊C25)) #42124409

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

Aliases

direct productC2×C3⋊(C3⋊(D31⋊C25))
unambiguous semidirect product(C2×C3)⋊(C3⋊(D31⋊C25))
unambiguous semidirect product(C2×C3⋊D93)⋊C25
unambiguous semidirect product(C2×C31⋊C25)⋊(C3⋊D3)

Splittings

derived, HallC32×C31 ⋊ C22×C25
HallC32×C31⋊C25 ⋊ C22
HallC2×C3⋊D93 ⋊ C25
HallC31⋊C25 ⋊ C2×C3⋊D3
SylowC31 ⋊ C2×C3⋊D3×C25
SylowC32 ⋊ C2×D31⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(C3⋊(D31⋊C5))
commutator, hypocenterC32×C31C22×C25
FrattiniC5C2×C3⋊(C3⋊(D31⋊C5))
Fitting, socleC2×C32×C5×C31C2×C5
prime radicalC2×C5×C3⋊D93C5
cosocleC32×C5×C31C22×C5
LCSG ▷ C32×C31
UCSC1 ◁ C2×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

570 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 156);