Finite Group Databasebeta

← Prev (#23748669) Next (#23748671) →

C₁₇×D₃₁⋊C₉ #23748670

order	9486
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₇×D₃₁⋊C₉
unambiguous semidirect product	D₃₁⋊(C₉×C₁₇)
unambiguous semidirect product	(C₃₁⋊C₉)⋊(C₂×C₁₇)
unambiguous semidirect product	(C₁₇×D₃₁)⋊C₉

Splittings

derived, Sylow	C₃₁ ⋊ C₂×C₉×C₁₇
Hall	C₁₇×C₃₁⋊C₉ ⋊ C₂
Hall	C₁₇×D₃₁ ⋊ C₉
Hall	C₁₇×C₃₁ ⋊ C₂×C₉
Hall	C₃₁⋊C₉ ⋊ C₂×C₁₇
Hall	D₃₁ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₇	D₃₁⋊C₃
commutator, hypocenter	C₃₁	C₂×C₉×C₁₇
Frattini	C₃	C₁₇×D₃₁⋊C₃
Fitting, socle	C₃×C₁₇×C₃₁	C₂×C₃
prime radical	C₃×C₁₇×D₃₁	C₃
cosocle	C₃×C₃₁	C₂×C₃×C₁₇
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

561 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₁₇×D₃₁⋊C₉, C₂×C₁₇×D₃₁⋊C₉
maximal normal subgroup of	D₁₇×D₃₁⋊C₉, C₂×C₁₇×D₃₁⋊C₉
maximal quotient of	C₁₇×Dic₃₁⋊C₉, C₂×C₁₇×D₃₁⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9486, 10);