C₁₁×D₅₃ #11923985

order	1166
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₁₁)

Splittings

Fitting, socle, Hall	C₁₁×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₁₁×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₁₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 64
transitive degree	μ_t(G) = 583

A minimal faithful permutation representation — 2 generators on 64 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);(13,64)(14,63)(15,62)(16,61)(17,60)(18,59)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁×#6157, C₁₁⋊#6157, D₁₁×D₅₃, …
maximal normal subgroup of	C₁₁×#6157, C₁₁⋊#6157, D₁₁×D₅₃, …
maximal quotient of	C₁₁×Dic₅₃, C₂×C₁₁×D₅₃, C₃×C₁₁×D₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1166, 2);

C11×D53 #11923985