C₅₉×C₂₃⋊C₁₁ #28417664

order	14927
isoclinism	isoclinic class of C₂₃⋊C₁₁
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₉×C₂₃⋊C₁₁
unambiguous semidirect product	C₂₃⋊(C₁₁×C₅₉)
unambiguous semidirect product	(C₂₃×C₅₉)⋊C₁₁

Splittings

Fitting, socle, Hall	C₂₃×C₅₉ ⋊ C₁₁
derived, Sylow	C₂₃ ⋊ C₁₁×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₅₉	C₂₃⋊C₁₁
commutator, cosocle, hypocenter	C₂₃	C₁₁×C₅₉
Frattini	C₁	G
Fitting, socle	C₂₃×C₅₉	C₁₁
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₅₉

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 82
transitive degree	μ_t(G) = 1357

A minimal faithful permutation representation — 2 generators on 82 points:

(2,3,4,6,9,10,15,18,5,8,12)(7,11,16,14,17,22,21,20,23,13,19)(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);(1,2,3,5,4,7,8,13,6,10,11,17,12,18,19,23,9,14,15,20,16,21,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₅₉×C₂₃⋊C₁₁, D₅₉×C₂₃⋊C₁₁, C₅₉×AGL(1,𝔽₂₃), …
maximal normal subgroup of	C₂×C₅₉×C₂₃⋊C₁₁, D₅₉×C₂₃⋊C₁₁, C₅₉×AGL(1,𝔽₂₃), …
maximal quotient of	C₂×C₅₉×C₂₃⋊C₁₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14927, 1);

C59×C23⋊C11 #28417664