Finite Group Databasebeta

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C3×#72223873 #72223876

order15840
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

general unitaryGU(2,𝔽11)
direct productC3×#72223873

Splittings

derivedSL(2,𝔽11) ⋊ C3×C4

Subgroups

subgroupG/H
center, Fitting, hypercenterC3×C4PGL(2,𝔽11)
commutator, hypocenterSL(2,𝔽11)C3×C4
FrattiniC4C3×PGL(2,𝔽11)
socleC2×C3#72223872
prime radicalC3×#72223869C2
cosocle#72223869C2×C3
LCSG ▷ SL(2,𝔽11)
UCSC1 ◁ C3×C4

147 conjugacy classes of subgroups; only the 12 normal subgroups are shown.

normal subgroups only

This group has 147 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.