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C₂×D₃×#3026 #72248404

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

Aliases

C₂×D₃×#3026

Splittings

Fitting	C₂×C₃×#3026 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#3026

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₃×#120
commutator, cosocle	C₂³×C₃	C₂⁶
Frattini	C₂³	C₂⁵×D₃
Fitting	C₂×C₃×#3026	C₂
socle	C₂²×C₃	C₂²×#120
hypercenter	C₂×#3026	D₃
hypocenter	C₃	C₂²×#3026
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂×#3026

48628 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	D₃×#394064, D₃×#498931, C₂×D₃×#33551, …
maximal normal subgroup of	D₃×#394064, D₃×#498931, C₂×D₃×#33551, …
maximal quotient of	D₃×#6470225, C₂×D₃×#32898

GAP

Past the SmallGroups library coverage — no SmallGroups id.