C₁₁×D₉₃ #14523301

order	2046
isoclinism	isoclinic class of D₉₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉₃
unambiguous semidirect product	C₃⋊(C₁₁×D₃₁)
unambiguous semidirect product	C₃₁⋊(D₃×C₁₁)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₃₁ ⋊ C₂
derived, Hall	C₃×C₃₁ ⋊ C₂×C₁₁
Hall	C₁₁×C₃₁ ⋊ D₃
Hall	C₃×C₁₁ ⋊ D₃₁
Sylow	C₃₁ ⋊ D₃×C₁₁
Sylow	C₃ ⋊ C₁₁×D₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₉₃
commutator, cosocle, hypocenter	C₃×C₃₁	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂
LCS	G ▷ C₃×C₃₁
UCS	C₁ ◁ 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);(13,14)(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

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

Relationships

maximal subgroup of	D₃×C₁₁×D₃₁, D₁₁×D₉₃, D₃₃⋊D₃₁, …
maximal normal subgroup of	D₃×C₁₁×D₃₁, D₁₁×D₉₃, D₃₃⋊D₃₁, …
maximal quotient of	C₁₁×Dic₉₃, C₂×C₁₁×D₉₃, C₇×C₁₁×D₉₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 7);

C11×D93 #14523301