Finite Group Databasebeta

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C₂×D₃×#3021 #72248097

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

Aliases

C₂×D₃×#3021

Splittings

Fitting	C₂×C₃×#3021 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#3021

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂×C₃×C₄	C₂⁶
Frattini	C₂×C₄	C₂⁵×D₃
Fitting	C₂×C₃×#3021	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂×#3021	D₃
hypocenter	C₃	C₂²×#3021
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ C₂×#3021

45572 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

174 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#23882, D₃×#449496, D₃×#498929, …
maximal normal subgroup of	C₂×D₃×#23882, D₃×#449496, D₃×#498929, …
maximal quotient of	D₃×#6437475

GAP

Past the SmallGroups library coverage — no SmallGroups id.