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C₁₇×C₉₇⋊C₉ #28415315

order	14841
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×C₉₇⋊C₉
unambiguous semidirect product	C₉₇⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×C₉₇)⋊C₉

Splittings

derived, Sylow	C₉₇ ⋊ C₉×C₁₇
Hall	C₁₇×C₉₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	C₉₇⋊C₃
commutator, hypocenter	C₉₇	C₉×C₁₇
Frattini	C₃	C₁₇×C₉₇⋊C₃
Fitting, socle, prime radical	C₃×C₁₇×C₉₇	C₃
cosocle	C₃×C₉₇	C₃×C₁₇
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₃×C₁₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 14841

Conjugacy classes & character table

1785 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₇×C₉₇⋊C₉, C₁₇×D₉₇⋊C₉, D₁₇×C₉₇⋊C₉, …
maximal normal subgroup of	C₂×C₁₇×C₉₇⋊C₉, C₁₇×D₉₇⋊C₉, D₁₇×C₉₇⋊C₉, …
maximal quotient of	C₂×C₁₇×C₉₇⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14841, 2);