Finite Group Databasebeta

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C3×#11773017 #72219102

order3456
automorphism?
homologyAbelianization (H1) = C2×C3×C32 · Schur multiplier (H2) = C2

Aliases

direct productC3×#11773017

Splittings

SylowC33 ⋊ C4⋊C32

Subgroups

subgroupG/H
center, hypercenterC3×C16GO+(4,𝔽2)
commutatorC3⋊D3C2×C3×C32
FrattiniC16C3×GO+(4,𝔽2)
FittingC33×C16D4
socleC2×C33C4⋊C16
prime radicalC2×C3×C3⋊D3C2×C16
cosocleC16×C3⋊D3C22×C3
hypocenterC32C3×C4⋊C32
LCSG ▷ C3⋊D3 ▷ C32
UCSC1 ◁ C3×C16

216 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 62 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

432 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×#72219099, C3×C32×GO+(4,𝔽2), C3×#72219115
maximal normal subgroup ofC3×#72219099, C3×C32×GO+(4,𝔽2), C3×#72219115

GAP

Past the SmallGroups library coverage — no SmallGroups id.