Finite Group Databasebeta

← Prev (#11929454) Next (#11929456) →

C₉×Dic₃₅ #11929455

order	1260
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₄×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×Dic₃₅

Splittings

derived, Hall	C₅×C₇ ⋊ C₄×C₉
Hall	C₅×C₇×C₉ ⋊ C₄
Hall	C₇×C₉ ⋊ Dic₅
Hall	C₅×C₉ ⋊ Dic₇
Sylow	C₇ ⋊ C₉×Dic₅
Sylow	C₅ ⋊ C₉×Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉	D₃₅
commutator, hypocenter	C₅×C₇	C₄×C₉
Frattini	C₂×C₃	C₃×D₃₅
Fitting	C₂×C₅×C₇×C₉	C₂
socle, prime radical, cosocle	C₂×C₃×C₅×C₇	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₉

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 1260

A minimal faithful permutation representation — 2 generators on 25 points:

(1,2,3,4,5,6,7,8,9)(10,11)(12,13)(14,15,16,17,18)(19,20,21,22,23,24,25);(10,12,11,13)(15,18)(16,17)(20,25)(21,24)(22,23)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×C₁₁×Dic₃₅, C₉×Dic₃₈₅, C₉×C₁₃×Dic₃₅, …
maximal normal subgroup of	C₉×C₁₁×Dic₃₅, C₉×C₁₃×Dic₃₅, C₉×C₁₇×Dic₃₅, …
maximal quotient of	C₉×C₁₁×Dic₃₅, C₉×Dic₃₈₅, C₉×C₁₃×Dic₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1260, 7);