D₉×C₁₂₁ #14546085

order	2178
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₂₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₉×C₁₂₁
unambiguous semidirect product	C₉⋊(C₂×C₁₂₁)

Splittings

Fitting, Hall	C₉×C₁₂₁ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂×C₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₂₁	D₉
commutator, hypocenter	C₉	C₂×C₁₂₁
Frattini, socle	C₃×C₁₁	D₃×C₁₁
Fitting	C₉×C₁₂₁	C₂
prime radical	C₁₁×D₉	C₁₁
cosocle	C₉×C₁₁	C₂×C₁₁
LCS	G ▷ C₉
UCS	C₁ ◁ C₁₂₁

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 130
transitive degree	μ_t(G) = 1089

A minimal faithful permutation representation — 2 generators on 130 points:

(1,2,3,4,5,6,7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130);(2,9)(3,8)(4,7)(5,6)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₉×D₁₂₁, C₂×D₉×C₁₂₁, D₉×C₁₂₁⋊C₅, …
maximal normal subgroup of	D₉×D₁₂₁, C₂×D₉×C₁₂₁, D₉×C₁₂₁⋊C₅, …
maximal quotient of	Dic₉×C₁₂₁, C₂×D₉×C₁₂₁, C₅×D₉×C₁₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2178, 2);

D9×C121 #14546085