Finite Group Databasebeta

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C₂×C₃⋊D₃×#87832 #72259986

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂×C₃⋊D₃×#87832

Splittings

Hall	C₃²×C₅² ⋊ C₂²×C₄⋊C₄
Sylow	C₅² ⋊ C₂×C₄⋊C₄×C₃⋊D₃
Sylow	C₃² ⋊ C₂²×#87832

Subgroups

	subgroup	G/H
center, hypercenter	C₂²	C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
commutator	C₂×C₃²×C₅²	C₂³×C₄
Frattini	C₂	C₂×C₃⋊D₃×D₅⋊AGL(1,𝔽₅)
Fitting, socle	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₂²×C₃⋊D₃×C₅⋊D₅	C₂²
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
hypocenter	C₃²×C₅²	C₂²×C₄⋊C₄
LCS	G ▷ C₂×C₃²×C₅² ▷ C₃²×C₅²
UCS	C₁ ◁ C₂²

6432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 360

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃⋊D₃×#11717375
maximal normal subgroup of	C₂×C₃⋊D₃×#11717375

GAP

Past the SmallGroups library coverage — no SmallGroups id.