C₁₁×D₁₇₁ #16836770

order	3762
isoclinism	isoclinic class of D₁₇₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₁₇₁
unambiguous semidirect product	C₉⋊(C₁₁×D₁₉)
unambiguous semidirect product	C₁₉⋊(C₁₁×D₉)

Splittings

Fitting, Hall	C₉×C₁₁×C₁₉ ⋊ C₂
derived, Hall	C₉×C₁₉ ⋊ C₂×C₁₁
Hall	C₁₁×C₁₉ ⋊ D₉
Hall	C₉×C₁₁ ⋊ D₁₉
Sylow	C₁₉ ⋊ C₁₁×D₉
Sylow	C₉ ⋊ C₁₁×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₁₇₁
commutator, cosocle, hypocenter	C₉×C₁₉	C₂×C₁₁
Frattini	C₃	C₁₁×D₅₇
Fitting	C₉×C₁₁×C₁₉	C₂
socle	C₃×C₁₁×C₁₉	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1881

A minimal faithful permutation representation — 2 generators on 39 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);(13,20)(14,19)(15,18)(16,17)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₅×C₁₁×D₁₇₁, C₁₁×D₈₅₅, C₁₁⋊C₅×D₁₇₁, …
maximal normal subgroup of	C₅×C₁₁×D₁₇₁, C₁₁⋊C₅×D₁₇₁, C₇×C₁₁×D₁₇₁
maximal quotient of	C₅×C₁₁×D₁₇₁, C₁₁×D₈₅₅, C₇×C₁₁×D₁₇₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3762, 10);

C11×D171 #16836770