Finite Group Databasebeta

← Prev (#11762128) Next (#11762130) →

C4×C5×C3⋊(C3⋊D3) #11762129

order1080
isoclinismisoclinic class of C3⋊(C3⋊D3)
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C33

Aliases

direct productC4×C5×C3⋊(C3⋊D3)

Splittings

FittingC33×C4×C5 ⋊ C2
derived, SylowC33 ⋊ C2×C4×C5
HallC33×C5 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4×C5C3⋊(C3⋊D3)
commutator, hypocenterC33C2×C4×C5
FrattiniC2C2×C5×C3⋊(C3⋊D3)
FittingC33×C4×C5C2
socleC2×C33×C5C22
prime radicalC2×C5×C3⋊(C3⋊D3)C2
cosocleC2×C33C22×C5
LCSG ▷ C33
UCSC1 ◁ C4×C5

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 540

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 475);