Finite Group Databasebeta

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C₉×C₁₇×D₅₃ #30633947

order	16218
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×C₁₇×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₉×C₁₇)

Splittings

Fitting, Hall	C₉×C₁₇×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₉×C₁₇
Hall	C₁₇×C₅₃ ⋊ C₂×C₉
Hall	C₉×C₅₃ ⋊ C₂×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉×C₁₇	D₅₃
commutator, hypocenter	C₅₃	C₂×C₉×C₁₇
Frattini	C₃	C₃×C₁₇×D₅₃
Fitting	C₉×C₁₇×C₅₃	C₂
socle	C₃×C₁₇×C₅₃	C₂×C₃
prime radical	C₃×C₁₇×D₅₃	C₃
cosocle	C₃×C₅₃	C₂×C₃×C₁₇
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₉×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8109

Conjugacy classes & character table

4284 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×C₁₇×#6157, C₉×#16813360, C₉×D₁₇×D₅₃, …
maximal normal subgroup of	C₉×C₁₇×#6157, C₉×#16813360, C₉×D₁₇×D₅₃, …
maximal quotient of	C₉×C₁₇×Dic₅₃, C₂×C₉×C₁₇×D₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16218, 2);