C₁₁×C₃⋊D₃×D₈₃ #45659672

order	32868
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₁ · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₁₁×C₃⋊D₃×D₈₃
unambiguous semidirect product	(C₃×D₈₃)⋊(D₃×C₁₁)

Splittings

Fitting, socle, Hall	C₃²×C₁₁×C₈₃ ⋊ C₂²
derived, Hall	C₃²×C₈₃ ⋊ C₂²×C₁₁
Hall	C₁₁×C₈₃ ⋊ C₂×C₃⋊D₃
Hall	C₃²×C₁₁ ⋊ C₂×D₈₃
Sylow	C₈₃ ⋊ C₂×C₁₁×C₃⋊D₃
Sylow	C₃² ⋊ C₂×C₁₁×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	C₃⋊D₃×D₈₃
commutator, cosocle, hypocenter	C₃²×C₈₃	C₂²×C₁₁
Frattini	C₁	G
Fitting, socle	C₃²×C₁₁×C₈₃	C₂²
LCS	G ▷ C₃²×C₈₃
UCS	C₁ ◁ C₁₁

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 100
transitive degree	μ_t(G) = 8217

A minimal faithful permutation representation — 3 generators on 100 points:

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

Conjugacy classes & character table

2838 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32868, 59);

C11×C3⋊D3×D83 #45659672