Finite Group Databasebeta

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C₁₇×C₃⋊D₃×C₂₉ #22580034

order	8874
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₂₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₁₇×C₃⋊D₃×C₂₉
unambiguous semidirect product	C₃⋊(D₃×C₁₇×C₂₉)

Splittings

Fitting, socle, Hall	C₃²×C₁₇×C₂₉ ⋊ C₂
derived, Sylow	C₃² ⋊ C₂×C₁₇×C₂₉
Hall	C₃²×C₂₉ ⋊ C₂×C₁₇
Hall	C₃²×C₁₇ ⋊ C₂×C₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₂₉	C₃⋊D₃
commutator, hypocenter	C₃²	C₂×C₁₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₃²×C₁₇×C₂₉	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₁₇×C₂₉

48 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×C₃⋊D₃×D₂₉, C₃⋊D₃×C₂₉×D₁₇, C₃⋊D₃×D₄₉₃, …
maximal normal subgroup of	C₁₇×C₃⋊D₃×D₂₉, C₃⋊D₃×C₂₉×D₁₇, C₃⋊D₃×D₄₉₃, …
maximal quotient of	C₁₇×C₂₉×C₃⋊Dic₃, C₂×C₁₇×C₃⋊D₃×C₂₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8874, 17);