C₄₃×D₅₃ #17986958

order	4558
isoclinism	isoclinic class of D₅₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄₃×D₅₃
unambiguous semidirect product	C₅₃⋊(C₂×C₄₃)

Splittings

Fitting, socle, Hall	C₄₃×C₅₃ ⋊ C₂
derived, Sylow	C₅₃ ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	D₅₃
commutator, cosocle, hypocenter	C₅₃	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₄₃×C₅₃	C₂
LCS	G ▷ C₅₃
UCS	C₁ ◁ C₄₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 96
transitive degree	μ_t(G) = 2279

A minimal faithful permutation representation — 2 generators on 96 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)(44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96);(45,96)(46,95)(47,94)(48,93)(49,92)(50,91)(51,90)(52,89)(53,88)(54,87)(55,86)(56,85)(57,84)(58,83)(59,82)(60,81)(61,80)(62,79)(63,78)(64,77)(65,76)(66,75)(67,74)(68,73)(69,72)(70,71)

Conjugacy classes & character table

1204 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₄₃×D₅₃, C₄₃×D₁₅₉, D₅₃×C₄₃⋊C₃, …
maximal normal subgroup of	C₃×C₄₃×D₅₃, D₅₃×C₄₃⋊C₃, C₅×C₄₃×D₅₃, …
maximal quotient of	C₃×C₄₃×D₅₃, C₄₃×D₁₅₉, C₅×C₄₃×D₅₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4558, 2);

C43×D53 #17986958