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C₂×D₇×C₁₉⋊C₃ #13097607

order	1596
isoclinism	isoclinic class of D₇×C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×D₇×C₁₉⋊C₃

Splittings

Fitting, socle	C₂×C₇×C₁₉ ⋊ C₂×C₃
derived, Hall	C₇×C₁₉ ⋊ C₂²×C₃
Hall	C₂×D₇×C₁₉ ⋊ C₃
Hall	C₇×C₁₉⋊C₃ ⋊ C₂²
Sylow	C₁₉ ⋊ C₂×C₃×D₇
Sylow	C₇ ⋊ C₂²×C₁₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₇×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 266

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#14558803, C₂×#14558804, C₂×AGL(1,𝔽₇)×C₁₉⋊C₃, …
maximal normal subgroup of	C₂×#14558803, C₂×#14558804, C₂×AGL(1,𝔽₇)×C₁₉⋊C₃, …
maximal quotient of	C₂×D₇×#4294, D₃×D₇×C₁₉⋊C₃, C₂×C₃×D₇×C₁₉⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 30);