Finite Group Databasebeta

C22×C5×C3⋊(C3⋊C8) #13088103

order1440
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23×C3

Aliases

direct productC22×C5×C3⋊(C3⋊C8)

Splittings

derived, SylowC32 ⋊ C22×C5×C8
HallC32×C5 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4×C5C3⋊D3
commutator, hypocenterC32C22×C5×C8
FrattiniC4C22×C5×C3⋊D3
FittingC22×C32×C4×C5C2
socle, prime radicalC23×C32×C5C4
cosocleC32×C4C23×C5
LCSG ▷ C32
UCSC1 ◁ C22×C4×C5

456 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1440

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4420);