Finite Group Databasebeta

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C₁₇×D₉×C₂₉ #22580022

order	8874
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₉×C₂₉
unambiguous semidirect product	C₉⋊(C₂×C₁₇×C₂₉)

Splittings

Fitting, Hall	C₉×C₁₇×C₂₉ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₇×C₂₉
Hall	C₉×C₂₉ ⋊ C₂×C₁₇
Hall	C₉×C₁₇ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₂₉	D₉
commutator, hypocenter	C₉	C₂×C₁₇×C₂₉
Frattini	C₃	D₃×C₁₇×C₂₉
Fitting	C₉×C₁₇×C₂₉	C₂
socle	C₃×C₁₇×C₂₉	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₇×C₂₉

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2958 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₇×D₉×D₂₉, D₉×C₂₉×D₁₇, D₉×D₄₉₃, …
maximal normal subgroup of	C₁₇×D₉×D₂₉, D₉×C₂₉×D₁₇, D₉×D₄₉₃, …
maximal quotient of	C₁₇×C₂₉×Dic₉, C₂×C₁₇×D₉×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8874, 5);