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C₂×D₃×#2196 #72245117

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹¹

Aliases

C₂×D₃×#2196

Splittings

Fitting	C₂×C₃×#2196 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2196

Subgroups

	subgroup	G/H
center	C₂²	D₃×B(4,𝔽₂)
commutator, cosocle	C₂×C₃×D₄	C₂⁵
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#2196	C₂
socle	C₂²×C₃	C₂×B(4,𝔽₂)
hypercenter	C₂×#2196	D₃
hypocenter	C₃	C₂²×#2196
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ C₂×#2196

14484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 48

Conjugacy classes & character table

120 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×#511771, C₂×D₃×#33551, D₃×#7622880, …
maximal normal subgroup of	D₃×#511771, C₂×D₃×#33551, D₃×#7622880, …
maximal quotient of	D₃×#511771
automorphism group of	D₃×#100, #4745, #4746, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.