Finite Group Databasebeta

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C₂×D₃×#2121 #72248188

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

Aliases

C₂×D₃×#2121

Splittings

Fitting	C₂×C₃×#2121 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2121

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#99
commutator	C₂³×C₃	C₂⁴×C₄
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#2121	C₂
socle	C₂²×C₃	C₂²×#99
prime radical	C₂×D₃×#534	C₂
cosocle	C₂×C₃×D₄	C₂⁵
hypercenter	C₂×#2121	D₃
hypocenter	C₃	C₂²×#2121
LCS	G ▷ C₂³×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂×#2121

10676 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	D₃×#147567, D₃×#498931, D₃×#147819, …
maximal normal subgroup of	D₃×#147567, D₃×#498931, D₃×#147819, …
maximal quotient of	D₃×#496225

GAP

Past the SmallGroups library coverage — no SmallGroups id.