Finite Group Databasebeta

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C4×C3⋊#1084 #13048015

order1296
automorphism?
homologyAbelianization (H1) = C42 · Schur multiplier (H2) = C32×C4

Aliases

direct productC4×C3⋊#1084

Splittings

derived, SylowC3×H(3,𝔽3) ⋊ C42

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C3⋊(C3⋊D3)
commutator, hypocenterC3×H(3,𝔽3)C42
FrattiniC22×C3C2×C3⋊(C3⋊D3)
FittingC2×C3×C4×H(3,𝔽3)C2
socleC22×C32C2×C3⋊D3
prime radical, cosocleC22×C3×H(3,𝔽3)C22
LCSG ▷ C3×H(3,𝔽3)
UCSC1 ◁ C2×C3×C4

730 conjugacy classes of subgroups; only the 247 normal subgroups are shown.

normal subgroups only

This group has 730 conjugacy classes of subgroups — too many to draw. Only its 247 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) = 144

Conjugacy classes & character table

168 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 1733);