C₁₁×D₂₂₁ #18012965

order	4862
isoclinism	isoclinic class of D₂₂₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₂₂₁
unambiguous semidirect product	C₁₃⋊(C₁₁×D₁₇)
unambiguous semidirect product	C₁₇⋊(C₁₁×D₁₃)

Splittings

Fitting, socle, Hall	C₁₁×C₁₃×C₁₇ ⋊ C₂
derived, Hall	C₁₃×C₁₇ ⋊ C₂×C₁₁
Hall	C₁₁×C₁₇ ⋊ D₁₃
Hall	C₁₁×C₁₃ ⋊ D₁₇
Sylow	C₁₇ ⋊ C₁₁×D₁₃
Sylow	C₁₃ ⋊ C₁₁×D₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₂₂₁
commutator, cosocle, hypocenter	C₁₃×C₁₇	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃×C₁₇	C₂
LCS	G ▷ C₁₃×C₁₇
UCS	C₁ ◁ C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 2431

A minimal faithful permutation representation — 2 generators on 41 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);(13,24)(14,23)(15,22)(16,21)(17,20)(18,19)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×D₂₂₁, C₁₁×D₆₆₃, C₁₁×C₁₇⋊(D₁₃⋊C₃), …
maximal normal subgroup of	C₃×C₁₁×D₂₂₁, C₁₁×C₁₇⋊(D₁₃⋊C₃), C₅×C₁₁×D₂₂₁, …
maximal quotient of	C₃×C₁₁×D₂₂₁, C₁₁×D₆₆₃, C₅×C₁₁×D₂₂₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4862, 4);

C11×D221 #18012965