Finite Group Databasebeta

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C₁₇×Dic₁₁₇ #22547339

order	7956
isoclinism	isoclinic class of D₁₁₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×Dic₁₁₇
unambiguous semidirect product	C₉⋊(C₁₇×Dic₁₃)

Splittings

derived, Hall	C₉×C₁₃ ⋊ C₄×C₁₇
Hall	C₉×C₁₃×C₁₇ ⋊ C₄
Hall	C₁₃×C₁₇ ⋊ Dic₉
Hall	C₉×C₁₇ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ C₁₇×Dic₉
Sylow	C₉ ⋊ C₁₇×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₇	D₁₁₇
commutator, hypocenter	C₉×C₁₃	C₄×C₁₇
Frattini	C₂×C₃	C₁₇×D₃₉
Fitting	C₂×C₉×C₁₃×C₁₇	C₂
socle	C₂×C₃×C₁₃×C₁₇	D₃
LCS	G ▷ C₉×C₁₃
UCS	C₁ ◁ C₂×C₁₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7956, 11);