Finite Group Databasebeta

C4×(C3⋊D3)⋊C27 #14515938

order1944
isoclinismisoclinic class of (C3⋊D3)⋊C3
automorphism?
homologyAbelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2×C3

Aliases

direct productC4×(C3⋊D3)⋊C27
unambiguous semidirect product(C4×C3⋊D3)⋊C27

Splittings

FittingC4×C32⋊C27 ⋊ C2
derivedC32 ⋊ C2×C4×C27
SylowC32⋊C27 ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC4×C9(C3⋊D3)⋊C3
commutator, hypocenterC32C2×C4×C27
FrattiniC2×C3×C9C2×C3×D3
FittingC4×C32⋊C27C2
socleC2×C32C2×D3×C9
prime radicalC2×C3×C3⋊D3C2×C9
cosocleC2×C32×C9C22×C3
LCSG ▷ C32
UCSC1 ◁ C4×C9

150 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 216

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 332);