Finite Group Databasebeta

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D₃×D₇×#453 #72244367

order	5376
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂¹⁰

Aliases

D₃×D₇×#453

Splittings

Fitting	C₃×C₇×#453 ⋊ C₂²
Hall	C₃×C₇ ⋊ C₂²×#453
Sylow	C₇ ⋊ C₂×D₃×#453
Sylow	C₃ ⋊ C₂×D₇×#453

Subgroups

	subgroup	G/H
center	C₂	D₃×D₇×#120
commutator, cosocle	C₂×C₃×C₄×C₇	C₂⁵
Frattini	C₂×C₄	C₂³×D₃×D₇
Fitting	C₃×C₇×#453	C₂²
socle	C₂×C₃×C₇	C₂²×#120
hypercenter	#453	D₃×D₇
hypocenter	C₃×C₇	C₂²×#453
LCS	G ▷ C₂×C₃×C₄×C₇ ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #453

11340 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₇×#11864777, D₃×AGL(1,𝔽₇)×#453
maximal normal subgroup of	D₃×AGL(1,𝔽₇)×#453
maximal quotient of	D₇×#11864777

GAP

Past the SmallGroups library coverage — no SmallGroups id.