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C₉×D₅₉₅ #24924194

order	10710
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₅₉₅
unambiguous semidirect product	C₅⋊(C₉×D₁₁₉)
unambiguous semidirect product	C₁₇⋊(C₉×D₃₅)

Splittings

Fitting, Hall	C₅×C₇×C₉×C₁₇ ⋊ C₂
derived, Hall	C₅×C₇×C₁₇ ⋊ C₂×C₉
Hall	C₇×C₉×C₁₇ ⋊ D₅
Hall	C₅×C₉×C₁₇ ⋊ D₇
Hall	C₅×C₇×C₉ ⋊ D₁₇
Hall	C₉×C₁₇ ⋊ D₃₅
Hall	C₇×C₁₇ ⋊ C₉×D₅
Hall	C₅×C₁₇ ⋊ C₉×D₇
Hall	C₇×C₉ ⋊ D₈₅
Hall	C₅×C₉ ⋊ D₁₁₉
Hall	C₅×C₇ ⋊ C₉×D₁₇
Sylow	C₁₇ ⋊ C₉×D₃₅
Sylow	C₇ ⋊ C₉×D₈₅
Sylow	C₅ ⋊ C₉×D₁₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₅₉₅
commutator, hypocenter	C₅×C₇×C₁₇	C₂×C₉
Frattini	C₃	C₃×D₅₉₅
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle, cosocle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×D₅₉₅	C₃
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₉×D₁₇×D₃₅, C₉×D₇×D₈₅, C₉×D₅×D₁₁₉, …
maximal normal subgroup of	C₉×D₁₇×D₃₅, C₉×D₇×D₈₅, C₉×D₅×D₁₁₉, …
maximal quotient of	C₉×Dic₅₉₅, C₂×C₉×D₅₉₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 9);