C₃×D₁₁×C₃₁ #14523298

order	2046
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₁₁×C₃₁
unambiguous semidirect product	C₁₁⋊(C₂×C₃×C₃₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₃₁	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₃×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₃×C₃₁

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);(5,14)(6,13)(7,12)(8,11)(9,10)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×D₁₁×D₃₁, D₃×D₁₁×C₃₁, D₁₁×D₉₃, …
maximal normal subgroup of	C₃×D₁₁×D₃₁, D₃×D₁₁×C₃₁, D₁₁×D₉₃, …
maximal quotient of	C₃×C₃₁×Dic₁₁, C₂×C₃×D₁₁×C₃₁, C₃×C₇×D₁₁×C₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 4);

C3×D11×C31 #14523298