C₄₁×C₅⋊D₅ #14523323

order	2050
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₁ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₄₁×C₅⋊D₅
unambiguous semidirect product	C₅⋊(D₅×C₄₁)

Splittings

Fitting, socle, Hall	C₅²×C₄₁ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₄₁	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₄₁
Frattini	C₁	G
Fitting, socle	C₅²×C₄₁	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 51
transitive degree	μ_t(G) = 1025

A minimal faithful permutation representation — 3 generators on 51 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)(48,49)(50,51);(47,48,50,51,49);(42,43,45,46,44)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₁×#1043, #16861520, C₄₁×#1044, …
maximal normal subgroup of	C₄₁×#1043, #16861520, C₄₁×#1044, …
maximal quotient of	C₄₁×#1039, C₂×C₄₁×C₅⋊D₅, C₄₁×C₅⋊D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2050, 15);

C41×C5⋊D5 #14523323