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C₉×C₁₀₃⋊C₁₇ #30628783

order	15759
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₀₃⋊C₁₇
unambiguous semidirect product	(C₉×C₁₀₃)⋊C₁₇

Splittings

Fitting, Hall	C₉×C₁₀₃ ⋊ C₁₇
derived, Sylow	C₁₀₃ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	C₁₀₃⋊C₁₇
commutator, hypocenter	C₁₀₃	C₉×C₁₇
Frattini	C₃	C₃×C₁₀₃⋊C₁₇
Fitting	C₉×C₁₀₃	C₁₇
socle, cosocle	C₃×C₁₀₃	C₃×C₁₇
prime radical	C₃×C₁₀₃⋊C₁₇	C₃
LCS	G ▷ C₁₀₃
UCS	C₁ ◁ C₉

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 927

Conjugacy classes & character table

207 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₉×C₁₀₃⋊C₁₇, C₉×D₁₀₃⋊C₁₇, D₉×C₁₀₃⋊C₁₇, …
maximal normal subgroup of	C₂×C₉×C₁₀₃⋊C₁₇, C₉×D₁₀₃⋊C₁₇, D₉×C₁₀₃⋊C₁₇, …
maximal quotient of	C₂×C₉×C₁₀₃⋊C₁₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15759, 3);