Finite Group Databasebeta

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C₂×D₃×#2122 #72254294

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂×D₃×#2122

Splittings

Fitting	C₂×C₃×#2122 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2122

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#99
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#2122	C₂
socle	C₂²×C₃	C₂²×#99
prime radical	C₂×D₃×#535	C₂
cosocle	C₂×C₃×D₄	C₂⁵
hypercenter	C₂×#2122	D₃
hypocenter	C₃	C₂²×#2122
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#2122

9964 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

138 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#12755, C₂×D₃×#33553, D₃×#498888, …
maximal normal subgroup of	C₂×D₃×#12755, C₂×D₃×#33553, D₃×#498888, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.