Finite Group Databasebeta

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C₂×C₃⋊D₃×#509 #72222706

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹×C₃

Aliases

C₂×C₃⋊D₃×#509

Splittings

Fitting	C₂×C₃²×#509 ⋊ C₂
Sylow	C₃² ⋊ C₂²×#509

Subgroups

	subgroup	G/H
center	C₂²	C₂×D₈×C₃⋊D₃
commutator, cosocle	C₃²×C₈	C₂⁵
Frattini	C₈	C₂⁴×C₃⋊D₃
Fitting	C₂×C₃²×#509	C₂
socle	C₂²×C₃²	C₂²×D₈
hypercenter	C₂×#509	C₃⋊D₃
hypocenter	C₃²	C₂²×#509
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#509

7002 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₃⋊D₃×AGL(1,ℤ/16)
maximal normal subgroup of	C₂×C₃⋊D₃×AGL(1,ℤ/16)
maximal quotient of	C₂×C₃⋊D₃×#2177

GAP

Past the SmallGroups library coverage — no SmallGroups id.