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C₃×C₁₉×D₁₃₃ #29503162

order	15162
isoclinism	isoclinic class of D₁₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₃×C₁₉×D₁₃₃

Splittings

Fitting, socle, Hall	C₃×C₇×C₁₉² ⋊ C₂
derived	C₇×C₁₉ ⋊ C₂×C₃×C₁₉
Hall	C₇×C₁₉² ⋊ C₂×C₃
Hall	C₃×C₁₉² ⋊ D₇
Sylow	C₁₉² ⋊ C₃×D₇
Hall	C₃×C₇ ⋊ C₁₉×D₁₉
Sylow	C₇ ⋊ C₃×C₁₉×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	D₁₃₃
commutator, cosocle, hypocenter	C₇×C₁₉	C₂×C₃×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₉²	C₂
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₁₉

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 798

Conjugacy classes & character table

3876 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₇×C₁₉×D₁₉, C₃×D₁₉×D₁₃₃, C₃×D₁₃₃⋊D₁₉, …
maximal normal subgroup of	C₃×D₇×C₁₉×D₁₉, C₃×D₁₉×D₁₃₃, C₃×D₁₃₃⋊D₁₉, …
maximal quotient of	C₃×C₁₉×Dic₁₃₃, C₂×C₃×C₁₉×D₁₃₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15162, 97);