Finite Group Databasebeta

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C22×#64269⋊C3 #72242701

order3456
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C27×C3

Aliases

direct productC22×#64269⋊C3

Splittings

FittingC26×C32 ⋊ D3

Subgroups

subgroupG/H
centerC23C2×(C3⋊S4)⋊C3
commutator, cosocleC2×C3×A4C24×C3
FrattiniC2×C3C23×C3×S4
FittingC26×C32D3
socleC25×C3C2×C3×D3
hypercenterC24(C3⋊S4)⋊C3
hypocenterC3×A4C22×C3×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C23 ◁ C24

7373 conjugacy classes of subgroups; only the 318 normal subgroups are shown.

normal subgroups only

This group has 7373 conjugacy classes of subgroups — too many to draw. Only its 318 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

232 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC22×#72213301

GAP

Past the SmallGroups library coverage — no SmallGroups id.