Finite Group Databasebeta

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C₂×D₃×#2199 #72248589

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

C₂×D₃×#2199

Splittings

Fitting	C₂×C₃×#2199 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#2199

Subgroups

	subgroup	G/H
center	C₂²	D₃×B(4,𝔽₂)
commutator, cosocle	C₂×C₃×D₄	C₂⁵
Frattini	C₂×D₄	C₂⁴×D₃
Fitting	C₂×C₃×#2199	C₂
socle	C₂²×C₃	C₂×B(4,𝔽₂)
hypercenter	C₂×#2199	D₃
hypocenter	C₃	C₂²×#2199
LCS	G ▷ C₂×C₃×D₄ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂³ ◁ C₂²×D₄ ◁ C₂×#2199

9588 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

102 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×#33551
maximal normal subgroup of	C₂×D₃×#33551
maximal quotient of	D₃×#508087

GAP

Past the SmallGroups library coverage — no SmallGroups id.