Finite Group Databasebeta

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C2×#10619988 #13048955

order1296
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22×C32

Aliases

direct productC2×#10619988

Splittings

SylowC3×H(3,𝔽3) ⋊ C2×Q8

Subgroups

subgroupG/H
centerC22×C3C2×C3⋊(C3⋊D3)
commutator, cosocleC2×C3×H(3,𝔽3)C23
FrattiniC2×C3C22×C3⋊(C3⋊D3)
FittingC2×C3×C4×H(3,𝔽3)C2
socleC22×C32C2×C3⋊D3
prime radicalC22×C3×H(3,𝔽3)C22
hypercenterC2×C3×C4C3⋊(C3⋊D3)
hypocenterC3×H(3,𝔽3)C2×Q8
LCSG ▷ C2×C3×H(3,𝔽3) ▷ C3×H(3,𝔽3)
UCSC1 ◁ C22×C3 ◁ C2×C3×C4

914 conjugacy classes of subgroups; only the 251 normal subgroups are shown.

normal subgroups only

This group has 914 conjugacy classes of subgroups — too many to draw. Only its 251 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

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1296, 2673);