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C₃×C₁₉×#64425 #30660765

order	16758
isoclinism	isoclinic class of #64425
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃×C₇

Aliases

C₃×C₁₉×#64425

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#64425
commutator, cosocle, hypocenter	C₇²	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1197

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₉×#10596885, C₃×C₁₉⋊#10596885, C₃×C₁₉×#64418⋊C₂, …
maximal normal subgroup of	C₃×C₁₉×#10596885, C₃×C₁₉⋊#10596885, C₃×C₁₉×#64418⋊C₂, …
maximal quotient of	C₃×C₁₉×#10596875, C₂×C₃×C₁₉×#64425

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16758, 292);