Finite Group Databasebeta

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C₂×D₃×#2134 #72248064

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₃×#2134

Splittings

Fitting	C₂×C₃×#2134 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2134

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#99
commutator	C₂×C₃×C₄	C₂⁴×C₄
Frattini	C₂×Q₈	C₂⁴×D₃
Fitting	C₂×C₃×#2134	C₂
socle	C₂²×C₃	C₂²×#99
prime radical	C₂×D₃×#535	C₂
cosocle	C₂×C₃×Q₈	C₂⁵
hypercenter	C₂×#2134	D₃
hypocenter	C₃	C₂²×#2134
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#41 ◁ C₂×#2134

9884 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×#12711, D₃×#494622, C₂×D₃×#12755, …
maximal normal subgroup of	C₂×D₃×#12711, D₃×#494622, C₂×D₃×#12755, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.