C₂₃×C₈₉⋊C₁₁ #36376649

order	22517
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×C₈₉⋊C₁₁
unambiguous semidirect product	C₈₉⋊(C₁₁×C₂₃)

Splittings

Fitting, socle, Hall	C₂₃×C₈₉ ⋊ C₁₁
derived, Sylow	C₈₉ ⋊ C₁₁×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	C₈₉⋊C₁₁
commutator, cosocle, hypocenter	C₈₉	C₁₁×C₂₃
Frattini	C₁	G
Fitting, socle	C₂₃×C₈₉	C₁₁
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 112
transitive degree	μ_t(G) = 2047

A minimal faithful permutation representation — 2 generators on 112 points:

(2,3,4,6,9,14,22,13,21,33,51)(5,8,12,19,30,46,65,47,67,79,73)(7,11,17,27,42,60,78,76,57,52,28)(10,16,25,39,45,15,24,37,34,53,74)(18,29,44,63,80,61,64,82,83,81,88)(20,32,49,70,23,36,26,41,59,75,35)(31,48,68,84,66,77,71,55,40,58,54)(38,56,50,72,87,43,62,69,85,89,86)(90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112);(1,2,4,7,9,15,17,28,22,35,37,55,42,61,11,18,21,34,32,50,53,75,58,76,78,84,82,89,27,43,44,64,51,73,74,88,70,86,87,6,10,12,20,19,31,33,52,39,57,59,77,63,81,24,38,41,60,48,69,72,80,67,83,85,3,5,8,13,16,26,29,45,36,54,56,65,62,79,14,23,25,40,30,47,49,71,46,66,68)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22517, 2);

C23×C89⋊C11 #36376649