C₄₁×C₃₁⋊C₃ #16838377

order	3813
isoclinism	isoclinic class of C₃₁⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×C₃₁⋊C₃
unambiguous semidirect product	C₃₁⋊(C₃×C₄₁)
unambiguous semidirect product	(C₃₁×C₄₁)⋊C₃

Splittings

Fitting, socle, Hall	C₃₁×C₄₁ ⋊ C₃
derived, Sylow	C₃₁ ⋊ C₃×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	C₃₁⋊C₃
commutator, cosocle, hypocenter	C₃₁	C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₄₁	C₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₄₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 72
transitive degree	μ_t(G) = 1271

A minimal faithful permutation representation — 2 generators on 72 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)(43,44,46)(45,48,53)(47,51,50)(49,55,62)(52,58,60)(54,56,57)(59,65,69)(61,66,67)(63,70,64)(68,71,72);(42,43,45,49,56,46,50,57,64,70,53,60,67,55,63,62,69,72,65,48,54,61,68,71,58,44,47,52,59,66,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₄₁×C₃₁⋊C₃, C₄₁×C₂²⋊(C₃₁⋊C₃), C₅×C₄₁×C₃₁⋊C₃, …
maximal normal subgroup of	C₃×C₄₁×C₃₁⋊C₃, C₅×C₄₁×C₃₁⋊C₃, C₃₁⋊C₃×C₄₁⋊C₅, …
maximal quotient of	C₄₁×C₃₁⋊C₉, C₃×C₄₁×C₃₁⋊C₃, C₄₁×C₂²⋊(C₃₁⋊C₃), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3813, 1);

C41×C31⋊C3 #16838377