C₁₁×#3674 #13096896

order	1584
isoclinism	isoclinic class of #3672
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₁×#3674

Splittings

Hall	C₉×C₁₁ ⋊ Q₁₆
Sylow	C₉ ⋊ C₁₁×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₁	#611
commutator, cosocle	C₄×C₉	C₂²×C₁₁
Frattini	C₃×C₄	C₂×D₃×C₁₁
Fitting	Q₈×C₉×C₁₁	C₂
socle, prime radical	C₂×C₃×C₁₁	#67
hypercenter	Q₈×C₁₁	D₉
hypocenter	C₉	C₁₁×Q₁₆
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₁₁ ◁ C₄×C₁₁ ◁ Q₈×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)(12,13,16,18,20,19,14,17,15)(21,23,25,31)(22,26,28,35)(24,33,34,30)(27,36,32,29);(13,15)(14,18)(16,17)(19,20)(21,22,25,28)(23,29,31,36)(24,32,34,27)(26,33,35,30)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1584, 60);

C11×#3674 #13096896