Finite Group Databasebeta

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C₂×#72219819 #72269977

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹²

Aliases

C₂×#72219819

Splittings

Fitting	C₂×C₃×#12753 ⋊ C₂
Sylow	C₃ ⋊ C₂×#511790

Subgroups

	subgroup	G/H
center	C₂²	#10943959
commutator, cosocle	C₂²×C₃×D₄	C₂⁵
Frattini	C₂²×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#12753	C₂
socle	C₂²×C₃	#32898
hypercenter	C₂×#12753	D₃
hypocenter	C₃	C₂×#511790
LCS	G ▷ C₂²×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂×#12753

At least 15468 conjugacy classes of subgroups; only the 1279 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#511790
maximal normal subgroup of	C₂×D₃×#511790

GAP

Past the SmallGroups library coverage — no SmallGroups id.