Finite Group Databasebeta

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C₂×#72240984 #72344197

order	6144
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×#72240984

Splittings

C₂×#10574874 ⋊ D₃

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂×#11713201
commutator, cosocle	#5950	C₂⁵
Frattini	C₂²×C₄	C₂⁴×S₄
Fitting	C₂×#10574874	D₃
hypercenter	C₂×#41	#1020⋊C₂
hypocenter	#997	C₂³×D₄
LCS	G ▷ #5950 ▷ #997
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#41

At least 21805 conjugacy classes of subgroups; only the 691 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

164 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.