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C₃×C₁₁×D₇×C₁₉ #22578607

order	8778
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₁₁×D₇×C₁₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁×C₁₉	D₇
commutator, hypocenter	C₇	C₂×C₃×C₁₁×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₁×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₁×C₁₉

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3135 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×D₇×D₁₉, C₃×D₇×C₁₉×D₁₁, C₃×D₇×D₂₀₉, …
maximal normal subgroup of	C₃×C₁₁×D₇×D₁₉, C₃×D₇×C₁₉×D₁₁, C₃×D₇×D₂₀₉, …
maximal quotient of	C₃×C₁₁×C₁₉×Dic₇, C₂×C₃×C₁₁×D₇×C₁₉, C₉×C₁₁×D₇×C₁₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 9);