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C₂×D₃×#2032 #72270299

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

C₂×D₃×#2032

Splittings

Fitting	C₂×C₃×#2032 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2032

Subgroups

	subgroup	G/H
center	C₂²	D₃×#393
commutator, cosocle	C₂⁴×C₃	C₂⁵
Frattini	C₂⁴	C₂⁴×D₃
Fitting	C₂×C₃×#2032	C₂
socle	C₂²×C₃	C₂×#393
prime radical	C₂³×D₃×D₄	C₂²
hypercenter	C₂×#2032	D₃
hypocenter	C₃	C₂²×#2032
LCS	G ▷ C₂⁴×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂×#2032

9868 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×#404015, C₂×D₃×#23996
maximal normal subgroup of	D₃×#404015, C₂×D₃×#23996

GAP

Past the SmallGroups library coverage — no SmallGroups id.