C₈₉×C₂₃⋊C₁₁ #36376648

order	22517
isoclinism	isoclinic class of C₂₃⋊C₁₁
automorphism	?
homology	Abelianization (H₁) = C₁₁×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

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

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:

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

Conjugacy classes & character table

1157 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22517, 1);

C89×C23⋊C11 #36376648