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C₂×C₉×D₁₃₃ #18012144

order	4788
isoclinism	isoclinic class of D₁₃₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×D₁₃₃

Splittings

Fitting	C₂×C₇×C₉×C₁₉ ⋊ C₂
derived, Hall	C₇×C₁₉ ⋊ C₂²×C₉
Hall	C₇×C₉×C₁₉ ⋊ C₂²
Hall	C₉×C₁₉ ⋊ C₂×D₇
Hall	C₇×C₉ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ C₂×C₉×D₇
Sylow	C₇ ⋊ C₂×C₉×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₁₃₃
commutator, hypocenter	C₇×C₁₉	C₂²×C₉
Frattini	C₃	C₂×C₃×D₁₃₃
Fitting	C₂×C₇×C₉×C₁₉	C₂
socle	C₂×C₃×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×D₁₃₃	C₃
cosocle	C₃×C₇×C₁₉	C₂²×C₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₉

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2394

Conjugacy classes & character table

1224 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₅×D₁₃₃, C₂×C₉×D₆₆₅, C₂×C₅×C₉×D₁₃₃, …
maximal normal subgroup of	C₂×C₅×C₉×D₁₃₃, C₂×C₇×C₉×D₁₃₃
maximal quotient of	C₉×D₅×D₁₃₃, C₂×C₉×D₆₆₅, C₂×C₅×C₉×D₁₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 60);