Finite Group Databasebeta

← Prev (#14519472) Next (#14519474) →

C4×C3⋊(C3⋊(C3⋊(C3⋊D3))) #14519473

order1944
isoclinismisoclinic class of C3⋊(C3⋊(C3⋊(C3⋊D3)))
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C310

Aliases

direct productC4×C3⋊(C3⋊(C3⋊(C3⋊D3)))

Splittings

FittingC35×C4 ⋊ C2
derived, SylowC35 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4C3⋊(C3⋊(C3⋊(C3⋊D3)))
commutator, hypocenterC35C2×C4
FrattiniC2C2×C3⋊(C3⋊(C3⋊(C3⋊D3)))
FittingC35×C4C2
socle, cosocleC2×C35C22
prime radicalC2×C3⋊(C3⋊(C3⋊(C3⋊D3)))C2
LCSG ▷ C35
UCSC1 ◁ C4

21312 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 972

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3867);