Finite Group Databasebeta

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C₁₇×Dic₁₃⋊C₉ #22547331

order	7956
isoclinism	isoclinic class of D₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₁₇)
unambiguous semidirect product	(C₁₇×Dic₁₃)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₁₇
Hall	C₁₇×C₁₃⋊C₉ ⋊ C₄
Hall	C₁₇×Dic₁₃ ⋊ C₉
Hall	C₁₃×C₁₇ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₁₇
Hall	Dic₁₃ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₁₇
Frattini	C₂×C₃	C₁₇×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃×C₁₇	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

816 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 3);