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C₂×#69310 #10948627

order	768
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

Fitting	C₂×C₃×#365 ⋊ C₂
Sylow	C₃ ⋊ C₂×AGL(1,ℤ/16)

Subgroups

	subgroup	G/H
center	C₂²	#4869
commutator	C₃×C₈	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₃
Fitting	C₂×C₃×#365	C₂
socle	C₂²×C₃	#442
prime radical	C₂×#4908	C₂
cosocle	C₂×C₃×C₈	C₂⁴
hypercenter	C₂×#365	D₃
hypocenter	C₃	C₂×AGL(1,ℤ/16)
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#365

710 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 96

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×AGL(1,ℤ/16), #72219834, #72219839, …
maximal normal subgroup of	C₂×D₃×AGL(1,ℤ/16), #72219834, #72219839, …
maximal quotient of	#72219834, C₂×#11797950, D₃×#69310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(768, 323008);