Finite Group Databasebeta

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C₂×#72220683 #72344060

order	6144
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁶

Aliases

C₂×#72220683

Splittings

C₂×#7630939 ⋊ D₃

Subgroups

	subgroup	G/H
center	C₂²	C₂³×#1020⋊C₂
commutator, cosocle	C₂×C₂²⋊A₄	C₂⁶
Frattini	C₂³	C₂⁵×S₄
Fitting	C₂×#7630939	D₃
socle	C₂⁴	C₂⁴×S₄
hypercenter	C₂²×D₄	#1020⋊C₂
hypocenter	C₂²⋊A₄	C₂²×H(5,𝔽₂)
LCS	G ▷ C₂×C₂²⋊A₄ ▷ C₂²⋊A₄
UCS	C₁ ◁ C₂² ◁ C₂²×D₄

Only the 3660 normal subgroups are shown; non-normal subgroups are omitted.

Full subgroup data →

Conjugacy classes & character table

244 conjugacy classes — view the full character table.

Relationships

maximal quotient of

C₂×#72247039

GAP

Past the SmallGroups library coverage — no SmallGroups id.