Finite Group Databasebeta

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C4×C3⋊(C3⋊#272) #14519011

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

Aliases

direct productC4×C3⋊(C3⋊#272)

Splittings

FittingC32×C4×H(3,𝔽3) ⋊ C2
derived, SylowC32×H(3,𝔽3) ⋊ C2×C4

Subgroups

subgroupG/H
center, hypercenterC3×C4C3⋊(C3⋊(C3⋊D3))
commutator, hypocenterC32×H(3,𝔽3)C2×C4
FrattiniC2×C3C2×C3⋊(C3⋊(C3⋊D3))
FittingC32×C4×H(3,𝔽3)C2
socleC2×C33C2×C3⋊D3
prime radicalC2×C3⋊(C3⋊#272)C2
cosocleC2×C32×H(3,𝔽3)C22
LCSG ▷ C32×H(3,𝔽3)
UCSC1 ◁ C3×C4

2664 conjugacy classes of subgroups; only the 659 normal subgroups are shown.

normal subgroups only

This group has 2664 conjugacy classes of subgroups — too many to draw. Only its 659 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, 3405);