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C₂×C₃×C₅×D₇×C₁₉ #22547762

order	7980
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₅×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₃×C₅×D₇×C₁₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₅×C₁₉	D₇
commutator, hypocenter	C₇	C₂²×C₃×C₅×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅×C₇×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₃×C₅×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₅×C₁₉×D₇⋊C₉, C₂×C₅×#14558784, C₂×C₅×#14558785, …
maximal normal subgroup of	C₂×C₅×C₁₉×D₇⋊C₉, C₂×C₅×#14558784, C₂×C₅×#14558785, …
maximal quotient of	C₂×C₅×C₉×D₇×C₁₉, C₃×C₅×D₃×D₇×C₁₉, C₂×C₃²×C₅×D₇×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 187);