Finite Group Databasebeta

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D₃×#13104700 #72231236

order	9600
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

D₃×#13104700

Splittings

Fitting	C₃×C₄²×C₅² ⋊ C₂×C₄
Hall	C₃×C₅² ⋊ C₂×#384
Sylow	C₅² ⋊ D₃×#384
Sylow	C₃ ⋊ C₂×#13104700

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×D₃×#1043
commutator, socle	C₂²×C₃×C₅²	C₂³×C₄
Fitting	C₃×C₄²×C₅²	C₂×C₄
prime radical	C₂²×D₃×C₅⋊D₅	C₂³
cosocle	C₂²×C₃×C₅⋊D₅	C₂⁴
hypercenter	C₄²	D₃×#1043
hypocenter	C₃×C₅²	C₂×#384
LCS	G ▷ C₂²×C₃×C₅² ▷ C₃×C₅²
UCS	C₁ ◁ C₂² ◁ C₄²

7104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1200

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×#127×#1043
maximal normal subgroup of	D₃×#127×#1043

GAP

Past the SmallGroups library coverage — no SmallGroups id.