Finite Group Databasebeta

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D₄×C₃⋊D₃×#1043 #72230629

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

Aliases

D₄×C₃⋊D₃×#1043

Splittings

Fitting	C₃²×C₅²×D₄ ⋊ C₂×C₄
Hall	C₃²×C₅² ⋊ C₂×C₄×D₄
Sylow	C₅² ⋊ C₄×D₄×C₃⋊D₃
Sylow	C₃² ⋊ C₂×D₄×#1043

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂²×C₃⋊D₃×#1043
commutator, socle	C₂×C₃²×C₅²	C₂³×C₄
Fitting	C₃²×C₅²×D₄	C₂×C₄
prime radical	D₄×C₃⋊D₃×C₅⋊D₅	C₂
cosocle	C₂×C₃²×C₅⋊D₅	C₂⁴
hypercenter	D₄	C₃⋊D₃×#1043
hypocenter	C₃²×C₅²	C₂×C₄×D₄
LCS	G ▷ C₂×C₃²×C₅² ▷ C₃²×C₅²
UCS	C₁ ◁ C₂ ◁ D₄

10224 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 900

Conjugacy classes & character table

300 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
maximal quotient of	C₂×D₄×C₃⋊D₃×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.