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C₃×C₁₉×#64422 #30660775

order	16758
isoclinism	isoclinic class of #64422
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₁₉×#64422

Splittings

Fitting, socle	C₃×C₇²×C₁₉ ⋊ C₂×C₃
derived, Sylow	C₇² ⋊ C₂×C₃²×C₁₉
Hall	C₃×C₁₉×#3862 ⋊ C₂
Hall	C₇×D₇×C₁₉ ⋊ C₃²
Hall	C₇²×C₁₉ ⋊ C₂×C₃²
Hall	C₃×#3862 ⋊ C₂×C₁₉
Hall	C₇×D₇ ⋊ C₃²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#64422
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₁₉×#64422, C₃×C₁₉×#64422⋊C₂, C₃×#64422⋊D₁₉, …
maximal normal subgroup of	C₃×D₁₉×#64422, C₃×C₁₉×#64422⋊C₂, C₃×#64422⋊D₁₉, …
maximal quotient of	C₃×C₁₉×#10596872, C₂×C₃×C₁₉×#64422

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 302);