Finite Group Databasebeta

← Prev (#72255396) Next (#72255398) →

C₂×C₃⋊D₃×#12067 #72255397

order	9216
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₈ · Schur multiplier (H₂) = C₂¹⁰×C₃

Aliases

C₂×C₃⋊D₃×#12067

Splittings

Fitting	C₂×C₃²×#12067 ⋊ C₂
Sylow	C₃² ⋊ C₂²×#12067

Subgroups

	subgroup	G/H
center	C₂³	C₃⋊D₃×#442
commutator	C₃²×C₈	C₂⁴×C₈
Frattini	C₄×C₈	C₂⁴×C₃⋊D₃
Fitting	C₂×C₃²×#12067	C₂
socle	C₂³×C₃²	C₂×#442
prime radical	C₂²×C₃⋊D₃×D₁₆	C₄
cosocle	C₃²×C₄×C₈	C₂⁵
hypercenter	C₂×#12067	C₃⋊D₃
hypocenter	C₃²	C₂²×#12067
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#322 ◁ C₂×#12067

21150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2304

Conjugacy classes & character table

552 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.