Finite Group Databasebeta

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C2×C3×#4268⋊C3 #72246514

order3024
automorphism?
homologyAbelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3

Aliases

direct productC2×C3×#4268⋊C3

Splittings

FittingC23×C32×C7 ⋊ C2×C3
HallC32×ΓL(1,𝔽8) ⋊ C2×D4
SylowC7 ⋊ C2×C32×#67

Subgroups

subgroupG/H
centerC22×C3C2×C3⋊AGL(1,𝔽7)
commutator, cosocleC2×C3×C7C23×C32
FrattiniC2C22×C3×C3⋊AGL(1,𝔽7)
FittingC23×C32×C7C2×C3
socleC22×C32×C7C22×C3
hypercenterC23×C3C3⋊AGL(1,𝔽7)
hypocenterC3×C7C2×C32×D4
LCSG ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C22×C3 ◁ C23×C3

904 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 168

Conjugacy classes & character table

234 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#72222044, C2×C3×#67×AGL(1,𝔽7), C2×#72222036, …
maximal normal subgroup ofC2×#72222044, C2×C3×#67×AGL(1,𝔽7), C2×#72222036, …
maximal quotient ofC3×#72245538

GAP

Past the SmallGroups library coverage — no SmallGroups id.