C₄₁×C₃⋊C₁₆ #14520078

order	1968
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₁₆×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₁×C₃⋊C₁₆
unambiguous semidirect product	C₃⋊(C₁₆×C₄₁)

Splittings

derived, Sylow	C₃ ⋊ C₁₆×C₄₁
Hall	C₃×C₄₁ ⋊ C₁₆

Subgroups

	subgroup	G/H
center, hypercenter	C₈×C₄₁	D₃
commutator, hypocenter	C₃	C₁₆×C₄₁
Frattini	C₈	D₃×C₄₁
Fitting	C₃×C₈×C₄₁	C₂
socle, prime radical	C₂×C₃×C₄₁	C₈
cosocle	C₃×C₈	C₂×C₄₁
LCS	G ▷ C₃
UCS	C₁ ◁ C₈×C₄₁

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 1968

A minimal faithful permutation representation — 2 generators on 60 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)(45,46,47,50,48,51,53,56,49,52,54,57,55,58,59,60);(42,43,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×C₁₆×C₄₁, C₂×C₄₁×C₃⋊C₁₆
maximal normal subgroup of	D₃×C₁₆×C₄₁, C₂×C₄₁×C₃⋊C₁₆
maximal quotient of	C₂×C₄₁×C₃⋊C₁₆

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1968, 1);

C41×C3⋊C16 #14520078