Finite Group Databasebeta

← Prev (#24924191) Next (#24924193) →

C₇×C₉×D₈₅ #24924192

order	10710
isoclinism	isoclinic class of D₈₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₉×D₈₅
unambiguous semidirect product	C₅⋊(C₇×C₉×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₇×C₉×D₅)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₉	D₈₅
commutator, hypocenter	C₅×C₁₇	C₂×C₇×C₉
Frattini	C₃	C₃×C₇×D₈₅
Fitting	C₅×C₇×C₉×C₁₇	C₂
socle	C₃×C₅×C₇×C₁₇	C₂×C₃
prime radical	C₃×C₇×D₈₅	C₃
cosocle	C₃×C₅×C₁₇	C₂×C₃×C₇
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₇×C₉

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×C₉×#66775, C₇×C₉×#66776, C₉×C₇⋊#66775, …
maximal normal subgroup of	C₇×C₉×#66775, C₇×C₉×#66776, C₉×C₇⋊#66775, …
maximal quotient of	C₇×C₉×Dic₈₅, C₂×C₇×C₉×D₈₅

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10710, 7);