Finite Group Databasebeta

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C₂×D₃×#3018 #72258837

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁶ · Schur multiplier (H₂) = C₂¹⁵

Aliases

C₂×D₃×#3018

Splittings

Fitting	C₂×C₃×#3018 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#3018

Subgroups

	subgroup	G/H
center	C₂×C₄	D₃×#120
commutator, cosocle	C₂×C₃×C₄	C₂⁶
Frattini	C₂×C₄	C₂⁵×D₃
Fitting	C₂×C₃×#3018	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂×#3018	D₃
hypocenter	C₃	C₂²×#3018
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#3018

44804 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.