Finite Group Databasebeta

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C₂×#72221864 #72244192

order	5832
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂×#72221864

Splittings

Fitting	C₂×#10624900 ⋊ C₂²
Sylow	#10624900 ⋊ C₂³

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊D₃×AGL(1,ℤ/9)
commutator, cosocle, hypocenter	C₉×H(3,𝔽₃)	C₂³×C₃
Frattini	C₃²	C₂×C₃×D₃×C₃⋊D₃
Fitting	C₂×#10624900	C₂²
socle	C₂×C₃²	C₃×D₃×C₃⋊D₃
prime radical	C₂×D₉×#272	C₃
LCS	G ▷ C₉×H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₃

1313 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

200 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72221868
maximal quotient of	C₂×#72221872

GAP

Past the SmallGroups library coverage — no SmallGroups id.