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C₉×C₁₇×D₁₁₉ #49138762

order	36414
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₇×D₁₁₉
unambiguous semidirect product	C₁₇⋊(C₉×D₇×C₁₇)

Splittings

Fitting, Hall	C₇×C₉×C₁₇² ⋊ C₂
derived	C₇×C₁₇ ⋊ C₂×C₉×C₁₇
Hall	C₉×C₁₇² ⋊ D₇
Hall	C₇×C₁₇² ⋊ C₂×C₉
Sylow	C₁₇² ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ C₁₇×D₁₇
Sylow	C₇ ⋊ C₉×C₁₇×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₂×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×D₁₁₉
Fitting	C₇×C₉×C₁₇²	C₂
socle	C₃×C₇×C₁₇²	C₂×C₃
prime radical	C₃×C₁₇×D₁₁₉	C₃
cosocle	C₃×C₇×C₁₇	C₂×C₃×C₁₇
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₉×C₁₇

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2142

Conjugacy classes & character table

9333 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36414, 57);