Finite Group Databasebeta

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C3×#6495⋊C3 #72244597

order2016
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3

Aliases

direct productC3×#6495⋊C3

Splittings

FittingC2×C3×C7×D4 ⋊ C2×C3
Hall#6495 ⋊ C32
HallC3×ΓL(1,𝔽8) ⋊ AGL(1,ℤ/8)
SylowC7 ⋊ C32×AGL(1,ℤ/8)

Subgroups

subgroupG/H
centerC2×C3C2×(C22⋊D7)⋊C3
commutator, cosocleC4×C7C23×C32
FrattiniC4C22×C3×AGL(1,𝔽7)
FittingC2×C3×C7×D4C2×C3
socleC2×C3×C7C2×C3×D4
hypercenterC2×C3×D4AGL(1,𝔽7)
hypocenterC7C32×AGL(1,ℤ/8)
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

408 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 168

Conjugacy classes & character table

129 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#89849⋊C3, C3×AGL(1,ℤ/8)×AGL(1,𝔽7), C3×#89970⋊C3, …
maximal normal subgroup ofC3×#89849⋊C3, C3×AGL(1,ℤ/8)×AGL(1,𝔽7), C3×#89970⋊C3, …
maximal quotient of#72245395, ΓL(1,𝔽8)×#6495⋊C3, C3×#72245538

GAP

Past the SmallGroups library coverage — no SmallGroups id.