Finite Group Databasebeta

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C₂×C₃⋊D₃×#7333 #72255491

order	9216
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈ · Schur multiplier (H₂) = C₂⁵×C₃

Aliases

C₂×C₃⋊D₃×#7333

Splittings

Fitting	C₂×C₃²×#7333 ⋊ C₂
Sylow	C₃² ⋊ C₂²×#7333

Subgroups

	subgroup	G/H
center	C₂×C₄	C₃⋊D₃×#322
commutator	C₃²×C₈	C₂²×C₄×C₈
Frattini	#346	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#7333	C₂
socle	C₂²×C₃²	C₂×#1313
prime radical	C₂³×C₃⋊D₃	#347
cosocle	C₃²×#346	C₂⁴
hypercenter	C₂×#7333	C₃⋊D₃
hypocenter	C₃²	C₂²×#7333
LCS	G ▷ C₃²×C₈ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#346 ◁ C₂×#7333

4758 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 576

Conjugacy classes & character table

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.