C₄₇×D₄₃ #16860950

order	4042
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₇×D₄₃
unambiguous semidirect product	C₄₃⋊(C₂×C₄₇)

Splittings

Fitting, socle, Hall	C₄₃×C₄₇ ⋊ C₂
derived, Sylow	C₄₃ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₄₃×C₄₇	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₄₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 90
transitive degree	μ_t(G) = 2021

A minimal faithful permutation representation — 2 generators on 90 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)(48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90);(49,90)(50,89)(51,88)(52,87)(53,86)(54,85)(55,84)(56,83)(57,82)(58,81)(59,80)(60,79)(61,78)(62,77)(63,76)(64,75)(65,74)(66,73)(67,72)(68,71)(69,70)

Conjugacy classes & character table

1081 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄₇×D₄₃, C₄₇×D₁₂₉, C₄₇×D₄₃⋊C₃, …
maximal normal subgroup of	C₃×C₄₇×D₄₃, C₄₇×D₄₃⋊C₃, C₅×C₄₇×D₄₃, …
maximal quotient of	C₃×C₄₇×D₄₃, C₄₇×D₁₂₉, C₅×C₄₇×D₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4042, 1);

C47×D43 #16860950