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C₃×C₇×D₇×C₁₉⋊C₃ #30660758

order	16758
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₇×D₇×C₁₉⋊C₃

Splittings

Fitting, socle	C₃×C₇²×C₁₉ ⋊ C₂×C₃
derived	C₇×C₁₉ ⋊ C₂×C₃²×C₇
Hall	C₃×C₇²×C₁₉⋊C₃ ⋊ C₂
Hall	C₇×D₇×C₁₉ ⋊ C₃²
Hall	C₇²×C₁₉ ⋊ C₂×C₃²
Sylow	C₇² ⋊ C₂×C₃×C₁₉⋊C₃
Sylow	C₁₉ ⋊ C₃²×C₇×D₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	D₇×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₇

132 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 798

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₇×D₇×D₁₉⋊C₃, C₃×D₇×(C₁₉⋊C₃)⋊D₇, C₃×D₇²×C₁₉⋊C₃, …
maximal normal subgroup of	C₃×C₇×D₇×D₁₉⋊C₃, C₃×D₇×(C₁₉⋊C₃)⋊D₇, C₃×D₇²×C₁₉⋊C₃, …
maximal quotient of	C₃×C₇×Dic₇×C₁₉⋊C₃, C₂×C₃×C₇×D₇×C₁₉⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 285);