Finite Group Databasebeta

C4×C3⋊(C9⋊D9) #14517720

order1944
isoclinismisoclinic class of C3⋊(C9⋊D9)
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C32×C9

Aliases

direct productC4×C3⋊(C9⋊D9)

Splittings

FittingC3×C4×C92 ⋊ C2
derived, SylowC3×C92 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4C3⋊(C9⋊D9)
commutator, hypocenterC3×C92C2×C4
FrattiniC2×C32C2×C3⋊(C3⋊D3)
FittingC3×C4×C92C2
socleC2×C33C2×C3⋊D3
prime radicalC2×C3⋊(C9⋊D9)C2
cosocleC2×C3×C92C22
LCSG ▷ C3×C92
UCSC1 ◁ C4

1008 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, 2114);