C₄₇×D₄₁ #16838726

order	3854
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂×C₄₇)

Splittings

Fitting, socle, Hall	C₄₁×C₄₇ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₄₁×C₄₇	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₄₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 88
transitive degree	μ_t(G) = 1927

A minimal faithful permutation representation — 2 generators on 88 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88);(49,88)(50,87)(51,86)(52,85)(53,84)(54,83)(55,82)(56,81)(57,80)(58,79)(59,78)(60,77)(61,76)(62,75)(63,74)(64,73)(65,72)(66,71)(67,70)(68,69)

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄₇×D₄₁, C₄₇×D₁₂₃, C₅×C₄₇×D₄₁, …
maximal normal subgroup of	C₃×C₄₇×D₄₁, C₅×C₄₇×D₄₁, C₄₇×D₄₁⋊C₅, …
maximal quotient of	C₃×C₄₇×D₄₁, C₄₇×D₁₂₃, C₅×C₄₇×D₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3854, 1);

C47×D41 #16838726