C₂₃×C₄₁⋊C₅ #17989952

order	4715
isoclinism	isoclinic class of C₄₁⋊C₅
automorphism	?
homology	Abelianization (H₁) = C₅×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×C₄₁⋊C₅
unambiguous semidirect product	C₄₁⋊(C₅×C₂₃)
unambiguous semidirect product	(C₂₃×C₄₁)⋊C₅

Splittings

Fitting, socle, Hall	C₂₃×C₄₁ ⋊ C₅
derived, Sylow	C₄₁ ⋊ C₅×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂₃×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 64
transitive degree	μ_t(G) = 943

A minimal faithful permutation representation — 2 generators on 64 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,26,28,32,40)(27,30,36,47,58)(29,34,43,35,45)(31,38,46,57,44)(33,42,53,41,52)(37,48,59,63,56)(39,51,50,61,64)(49,60,54,62,55);(24,25,27,31,39,48,52,57,63,59,26,29,35,46,53,60,32,41,28,33,30,37,49,61,62,64,42,54,34,44,38,50,47,58,43,55,36,40,45,56,51)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₂₃×C₄₁⋊C₅, C₅×C₂₃×C₄₁⋊C₅, C₇×C₂₃×C₄₁⋊C₅
maximal normal subgroup of	C₃×C₂₃×C₄₁⋊C₅, C₅×C₂₃×C₄₁⋊C₅, C₇×C₂₃×C₄₁⋊C₅
maximal quotient of	C₃×C₂₃×C₄₁⋊C₅, C₂₃×C₄₁⋊C₂₅, C₅×C₂₃×C₄₁⋊C₅, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4715, 1);

C23×C41⋊C5 #17989952