Finite Group Databasebeta

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C₂×D₃×#7389 #72255389

order	3072
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×D₃×#7389

Splittings

Fitting	C₂×C₃×#7389 ⋊ C₂
Sylow	C₃ ⋊ C₂²×#7389

Subgroups

	subgroup	G/H
center	C₂²	D₃×#1333
commutator	C₃×C₁₆	C₂³×C₈
Frattini	#346	C₂³×D₃
Fitting	C₂×C₃×#7389	C₂
socle	C₂²×C₃	C₂×#1333
prime radical	C₂×D₃×#508	C₄
cosocle	C₃×#346	C₂⁴
hypercenter	C₂×#7389	D₃
hypocenter	C₃	C₂²×#7389
LCS	G ▷ C₃×C₁₆ ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#346 ◁ C₂×#7389

2762 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Conjugacy classes & character table

204 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×D₃×AGL(1,ℤ/32)
maximal normal subgroup of	C₂×D₃×AGL(1,ℤ/32)

GAP

Past the SmallGroups library coverage — no SmallGroups id.