Finite Group Databasebeta

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C2×C3⋊(C3⋊#1084) #14519018

order1944
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2×C35

Aliases

direct productC2×C3⋊(C3⋊#1084)
unambiguous semidirect product(C2×C3)⋊(C3⋊#1084)

Splittings

derived, SylowC32×H(3,𝔽3) ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC22×C3C3⋊(C3⋊(C3⋊D3))
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C2×C3⋊(C3⋊(C3⋊D3))
Fitting, prime radicalC22×C32×H(3,𝔽3)C2
socleC22×C33C3⋊D3
cosocleC2×C32×H(3,𝔽3)C22
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C22×C3

2808 conjugacy classes of subgroups; only the 1093 normal subgroups are shown.

normal subgroups only

This group has 2808 conjugacy classes of subgroups — too many to draw. Only its 1093 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

216 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 3412);