C₉×D₁₁₉ #14523872

order	2142
isoclinism	isoclinic class of D₁₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₉×D₁₁₉
unambiguous semidirect product	C₁₇⋊(C₉×D₇)

Splittings

Fitting, Hall	C₇×C₉×C₁₇ ⋊ C₂
derived, Hall	C₇×C₁₇ ⋊ C₂×C₉
Hall	C₉×C₁₇ ⋊ D₇
Hall	C₇×C₉ ⋊ D₁₇
Sylow	C₁₇ ⋊ C₉×D₇
Sylow	C₇ ⋊ C₉×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₉	D₁₁₉
commutator, hypocenter	C₇×C₁₇	C₂×C₉
Frattini	C₃	C₃×D₁₁₉
Fitting	C₇×C₉×C₁₇	C₂
socle, cosocle	C₃×C₇×C₁₇	C₂×C₃
prime radical	C₃×D₁₁₉	C₃
LCS	G ▷ C₇×C₁₇
UCS	C₁ ◁ C₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 1071

A minimal faithful permutation representation — 2 generators on 33 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16)(17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(11,16)(12,15)(13,14)(18,33)(19,32)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₉×D₇×D₁₇, D₉×D₁₁₉, D₆₃⋊D₁₇, …
maximal normal subgroup of	C₉×D₇×D₁₇, D₉×D₁₁₉, D₆₃⋊D₁₇, …
maximal quotient of	C₉×Dic₁₁₉, C₂×C₉×D₁₁₉, C₉×D₈₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2142, 8);

C9×D119 #14523872