C₄₃×C₅⋊D₅ #14524121

order	2150
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₄₃×C₅⋊D₅
unambiguous semidirect product	C₅⋊(D₅×C₄₃)

Splittings

Fitting, socle, Hall	C₅²×C₄₃ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₄₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₄₃
Frattini	C₁	G
Fitting, socle	C₅²×C₄₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₄₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 53
transitive degree	μ_t(G) = 1075

A minimal faithful permutation representation — 3 generators on 53 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)(45,46)(47,48)(50,51)(52,53);(49,50,52,53,51);(44,45,47,48,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₃×#1043, C₄₃⋊#1043, C₄₃×#1044, …
maximal normal subgroup of	C₄₃×#1043, C₄₃⋊#1043, C₄₃×#1044, …
maximal quotient of	C₄₃×#1039, C₂×C₄₃×C₅⋊D₅, C₄₃×C₅⋊D₃₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2150, 9);

C43×C5⋊D5 #14524121