C₅₃×D₄₁ #16864720

order	4346
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×D₄₁
unambiguous semidirect product	C₄₁⋊(C₂×C₅₃)

Splittings

Fitting, socle, Hall	C₄₁×C₅₃ ⋊ C₂
derived, Sylow	C₄₁ ⋊ C₂×C₅₃

Subgroups

	subgroup	G/H
center, hypercenter	C₅₃	D₄₁
commutator, cosocle, hypocenter	C₄₁	C₂×C₅₃
Frattini	C₁	G
Fitting, socle	C₄₁×C₅₃	C₂
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₅₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 94
transitive degree	μ_t(G) = 2173

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

Conjugacy classes & character table

1166 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₅₃×D₄₁, C₅₃×D₁₂₃, C₅×C₅₃×D₄₁, …
maximal normal subgroup of	C₃×C₅₃×D₄₁, C₅×C₅₃×D₄₁, C₅₃×D₄₁⋊C₅, …
maximal quotient of	C₃×C₅₃×D₄₁, C₅₃×D₁₂₃, C₅×C₅₃×D₄₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4346, 1);

C53×D41 #16864720