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D₃×D₇×#41 #13062265

order	1344
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁹

Aliases

D₃×D₇×#41

Splittings

Fitting	C₃×C₇×#41 ⋊ C₂²
Hall	C₃×C₇ ⋊ C₂²×#41
Sylow	C₇ ⋊ C₂×D₃×#41
Sylow	C₃ ⋊ C₂×D₇×#41

Subgroups

	subgroup	G/H
center	C₄	C₂²×D₃×D₇
commutator, socle, cosocle	C₂×C₃×C₇	C₂⁵
Frattini	C₂	C₂³×D₃×D₇
Fitting	C₃×C₇×#41	C₂²
hypercenter	#41	D₃×D₇
hypocenter	C₃×C₇	C₂²×#41
LCS	G ▷ C₂×C₃×C₇ ▷ C₃×C₇
UCS	C₁ ◁ C₄ ◁ #41

1780 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 168

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×D₇×H(5,𝔽₂), D₃×D₇×AGL(1,ℤ/8), D₃×D₇×#104, …
maximal normal subgroup of	D₃×D₇×H(5,𝔽₂), D₃×D₇×AGL(1,ℤ/8), D₃×D₇×#104, …
maximal quotient of	D₇×#64306, D₇×#64312, D₃×#13096688, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1344, 11554);