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C₂×C₁₉×D₇⋊C₉ #18012120

order	4788
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×D₇⋊C₉
unambiguous semidirect product	D₇⋊(C₂×C₉×C₁₉)
unambiguous semidirect product	(C₂×D₇)⋊(C₉×C₁₉)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂²×C₁₉)
unambiguous semidirect product	(C₂×C₇⋊C₉)⋊(C₂×C₁₉)

Splittings

derived, Sylow	C₇ ⋊ C₂²×C₉×C₁₉
Hall	C₁₉×C₇⋊C₉ ⋊ C₂²
Hall	C₂×D₇×C₁₉ ⋊ C₉
Hall	C₇×C₁₉ ⋊ C₂²×C₉
Hall	C₇⋊C₉ ⋊ C₂²×C₁₉
Hall	C₂×D₇ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₁₉×AGL(1,𝔽₇)
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×D₇×C₁₉	C₃
cosocle	C₃×C₇	C₂²×C₃×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₅×C₁₉×D₇⋊C₉, C₂×C₅×C₁₉×D₇⋊C₉, C₂×C₁₉×C₅⋊(D₇⋊C₉), …
maximal normal subgroup of	C₂×C₅×C₁₉×D₇⋊C₉, C₂×C₇×C₁₉×D₇⋊C₉
maximal quotient of	D₅×C₁₉×D₇⋊C₉, C₂×C₅×C₁₉×D₇⋊C₉, C₂×C₁₉×C₅⋊(D₇⋊C₉), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 36);