C₃×C₁₁×D₃₁ #14523297

order	2046
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₃×C₁₁×D₃₁

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₃₁ ⋊ C₂
derived, Sylow	C₃₁ ⋊ C₂×C₃×C₁₁
Hall	C₁₁×C₃₁ ⋊ C₂×C₃
Hall	C₃×C₃₁ ⋊ C₂×C₁₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₁	D₃₁
commutator, cosocle, hypocenter	C₃₁	C₂×C₃×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₃×C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1023

A minimal faithful permutation representation — 2 generators on 45 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);(16,45)(17,44)(18,43)(19,42)(20,41)(21,40)(22,39)(23,38)(24,37)(25,36)(26,35)(27,34)(28,33)(29,32)(30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₁₁×D₃₁, D₃×C₁₁×D₃₁, D₃₁×D₃₃, …
maximal normal subgroup of	C₃×D₁₁×D₃₁, D₃×C₁₁×D₃₁, D₃₁×D₃₃, …
maximal quotient of	C₃×C₁₁×Dic₃₁, C₂×C₃×C₁₁×D₃₁, C₃×C₇×C₁₁×D₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 3);

C3×C11×D31 #14523297