Finite Group Databasebeta

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C₁₃×C₁₇×Dic₉ #22547337

order	7956
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×C₁₇×Dic₉
unambiguous semidirect product	C₉⋊(C₄×C₁₃×C₁₇)

Splittings

derived, Sylow	C₉ ⋊ C₄×C₁₃×C₁₇
Hall	C₉×C₁₃×C₁₇ ⋊ C₄
Hall	C₉×C₁₇ ⋊ C₄×C₁₃
Hall	C₉×C₁₃ ⋊ C₄×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃×C₁₇	D₉
commutator, hypocenter	C₉	C₄×C₁₃×C₁₇
Frattini	C₂×C₃	D₃×C₁₃×C₁₇
Fitting	C₂×C₉×C₁₃×C₁₇	C₂
socle	C₂×C₃×C₁₃×C₁₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₃×C₁₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2652 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 9);