C₃₁×D₃₃ #14523302

order	2046
isoclinism	isoclinic class of D₃₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×D₃₃
unambiguous semidirect product	C₃⋊(D₁₁×C₃₁)
unambiguous semidirect product	C₁₁⋊(D₃×C₃₁)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₃₁ ⋊ C₂
derived, Hall	C₃×C₁₁ ⋊ C₂×C₃₁
Hall	C₁₁×C₃₁ ⋊ D₃
Hall	C₃×C₃₁ ⋊ D₁₁
Sylow	C₁₁ ⋊ D₃×C₃₁
Sylow	C₃ ⋊ D₁₁×C₃₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃₁	D₃₃
commutator, cosocle, hypocenter	C₃×C₁₁	C₂×C₃₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₃₁	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ 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);(33,34)(36,45)(37,44)(38,43)(39,42)(40,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃₁×D₃₃, D₃×D₁₁×C₃₁, D₃₃⋊D₃₁, …
maximal normal subgroup of	D₃₁×D₃₃, D₃×D₁₁×C₃₁, D₃₃⋊D₃₁, …
maximal quotient of	C₃₁×Dic₃₃, C₂×C₃₁×D₃₃, C₇×C₃₁×D₃₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2046, 8);

C31×D33 #14523302