Finite Group Databasebeta

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C₂×#10710645 #72269955

order	1536
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁹

Aliases

C₂×#10710645

Splittings

Fitting	C₂²×C₃×AΣL(1,𝔽₁₆) ⋊ C₂
Sylow	C₃ ⋊ C₂×#12687

Subgroups

	subgroup	G/H
center	C₂³	D₃×#99
commutator	C₂⁴×C₃	C₂³×C₄
Frattini	C₂²×D₄	C₂³×D₃
Fitting	C₂²×C₃×AΣL(1,𝔽₁₆)	C₂
socle	C₂³×C₃	C₂×#99
prime radical	C₂²×D₃×#120	C₂
cosocle	C₂²×C₃×D₄	C₂⁴
hypercenter	C₂²×AΣL(1,𝔽₁₆)	D₃
hypocenter	C₃	C₂×#12687
LCS	G ▷ C₂⁴×C₃ ▷ C₂²×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂²×AΣL(1,𝔽₁₆)

22592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72219817, C₂×#72219819, C₂×D₃×#12687
maximal normal subgroup of	C₂×#72219817, C₂×#72219819, C₂×D₃×#12687

GAP

Past the SmallGroups library coverage — no SmallGroups id.