Finite Group Databasebeta

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C₂×C₄×C₃⋊D₃×#1043 #72230555

order	14400
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁵×C₃×C₄

Aliases

C₂×C₄×C₃⋊D₃×#1043

Splittings

Fitting	C₂×C₃²×C₄×C₅² ⋊ C₂×C₄
derived, Hall	C₃²×C₅² ⋊ C₂²×C₄²
Sylow	C₅² ⋊ C₂×C₄²×C₃⋊D₃
Sylow	C₃² ⋊ C₂²×C₄×#1043

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄	C₃⋊D₃×#1043
commutator, hypocenter	C₃²×C₅²	C₂²×C₄²
Frattini	C₂	C₂²×C₃⋊D₃×#1043
Fitting	C₂×C₃²×C₄×C₅²	C₂×C₄
socle	C₂²×C₃²×C₅²	C₂²×C₄
prime radical	C₂²×C₃⋊D₃×C₅⋊D₅	C₂²
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
LCS	G ▷ C₃²×C₅²
UCS	C₁ ◁ C₂×C₄

11952 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1800

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×D₄×C₃⋊D₃×#1043
maximal normal subgroup of	C₂×D₄×C₃⋊D₃×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.