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C₃×D₅×C₁₃×C₁₉ #20301802

order	7410
isoclinism	isoclinic class of D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₅×C₁₃×C₁₉
unambiguous semidirect product	C₅⋊(C₂×C₃×C₁₃×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₉	D₅
commutator, hypocenter	C₅	C₂×C₃×C₁₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₁₃×C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₃×C₁₉×AGL(1,𝔽₅), C₃×C₁₃×C₁₉⋊AGL(1,𝔽₅), C₃×C₁₉×#63120, …
maximal normal subgroup of	C₃×C₁₃×C₁₉×AGL(1,𝔽₅), C₃×C₁₃×C₁₉⋊AGL(1,𝔽₅), C₃×C₁₉×#63120, …
maximal quotient of	C₃×C₁₃×C₁₉×Dic₅, C₂×C₃×D₅×C₁₃×C₁₉, C₉×D₅×C₁₃×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7410, 9);