C₁₁×Dic₄₁ #14268564

order	1804
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×Dic₄₁

Splittings

derived, Sylow	C₄₁ ⋊ C₄×C₁₁
Hall	C₁₁×C₄₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₁
commutator, hypocenter	C₄₁	C₄×C₁₁
Frattini	C₂	C₁₁×D₄₁
Fitting, socle, prime radical	C₂×C₁₁×C₄₁	C₂
cosocle	C₂×C₄₁	C₂×C₁₁
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₁₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 56
transitive degree	μ_t(G) = 1804

A minimal faithful permutation representation — 2 generators on 56 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);(12,14,13,15)(17,56)(18,55)(19,54)(20,53)(21,52)(22,51)(23,50)(24,49)(25,48)(26,47)(27,46)(28,45)(29,44)(30,43)(31,42)(32,41)(33,40)(34,39)(35,38)(36,37)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₁×Dic₄₁, C₁₁×Dic₂₈₇, C₁₁×#13093288, …
maximal normal subgroup of	C₇×C₁₁×Dic₄₁, C₁₂₁×Dic₄₁, C₁₁²×Dic₄₁, …
maximal quotient of	C₇×C₁₁×Dic₄₁, C₁₁×Dic₂₈₇, C₁₁×#13093288, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1804, 2);

C11×Dic41 #14268564