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C₁₁×D₇×C₁₉⋊C₃ #22578631

order	8778
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

C₁₁×D₇×C₁₉⋊C₃

Splittings

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

495 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₁₁×D₇×D₁₉⋊C₃, D₇×C₁₁⋊(D₁₉⋊C₃), D₇×D₁₁×C₁₉⋊C₃, …
maximal normal subgroup of	C₁₁×D₇×D₁₉⋊C₃, D₇×C₁₁⋊(D₁₉⋊C₃), D₇×D₁₁×C₁₉⋊C₃, …
maximal quotient of	C₁₁×Dic₇×C₁₉⋊C₃, C₂×C₁₁×D₇×C₁₉⋊C₃, C₁₁×D₇×#4294, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 33);