Finite Group Databasebeta

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C₂×#72221863 #72244190

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

Aliases

C₂×#72221863

Splittings

Fitting	C₂×#10624869 ⋊ C₂²
Sylow	#10624869 ⋊ C₂³

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	((C₃⋊D₃)⋊C₃)⋊D₃
commutator, cosocle, hypocenter	C₃²⋊H(3,𝔽₃)	C₂³×C₃
Frattini	C₃²	C₂×C₃×D₃×C₃⋊D₃
Fitting	C₂×#10624869	C₂²
socle	C₂×C₃²	C₃×D₃×C₃⋊D₃
prime radical	C₂×#11757730	C₃
LCS	G ▷ C₃²⋊H(3,𝔽₃)
UCS	C₁ ◁ C₂×C₉

1667 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

234 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.