C₁₁×Dic₃₆ #13096883

order	1584
isoclinism	isoclinic class of Dic₃₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×Dic₃₆

Splittings

Hall	C₉×C₁₁ ⋊ Q₁₆
Sylow	C₉ ⋊ C₁₁×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁	D₃₆
commutator, cosocle	C₄×C₉	C₂²×C₁₁
Frattini	C₃×C₄	C₂×D₃×C₁₁
Fitting	C₈×C₉×C₁₁	C₂
socle, prime radical	C₂×C₃×C₁₁	D₁₂
hypercenter	C₈×C₁₁	D₉
hypocenter	C₉	C₁₁×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ C₈×C₁₁

54 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 36
transitive degree	μ_t(G) = 1584

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14,15,16,17,18,19)(20,27,26,25,24,23,22,21)(28,29,30,31,32,33,34,35,36);(12,20,16,24)(13,21,17,25)(14,22,18,26)(15,23,19,27)(29,36)(30,35)(31,34)(32,33)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 47);

C11×Dic36 #13096883