#27187849

order	12928
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁵

Aliases

No aliases for this group.

Splittings

Sylow

C₁₀₁ ⋊ #2929

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂³×#87938
commutator, socle	C₂²×C₁₀₁	C₂³×C₄
Fitting	#123×C₁₀₁	C₄
prime radical	#20265685	C₂
cosocle	C₂×Dic₁₀₁	C₂⁴
hypercenter	#123	#87938
hypocenter	C₁₀₁	#2929
LCS	G ▷ C₂²×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂² ◁ #123

520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 121
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 4 generators on 121 points:

(1,2,6,12,22,36,54,38,24,14,5,8,16,28,42,58,72,60,44,27,11,18,30,46,64,76,86,78,63,41,21,32,48,66,80,90,96,89,75,57,35,50,68,82,92,98,101,95,85,71,53,51,69,83,93,99,100,97,87,73,55,33,49,67,81,91,94,88,77,59,37,19,31,47,65,79,84,74,62,43,23,9,17,29,45,61,70,56,40,26,13,3,7,15,25,39,52,34,20,10,4)(107,112)(111,117)(113,119)(118,121);(2,5,4,3)(6,11,10,9)(7,8,14,13)(12,21,20,19)(15,18,24,23)(16,27,26,17)(22,35,34,33)(25,32,38,37)(28,41,40,31)(29,30,44,43)(36,53,52,51)(39,50,54,55)(42,57,56,49)(45,48,60,59)(46,63,62,47)(58,71,70,69)(61,68,72,73)(64,75,74,67)(65,66,78,77)(76,85,84,83)(79,82,86,87)(80,89,88,81)(90,95,94,93)(91,92,96,97)(98,101,100,99)(106,108,109,114,110,115,116,120)(107,111,113,118,112,117,119,121);(2,4)(3,5)(6,10)(7,14)(8,13)(9,11)(12,20)(15,24)(16,26)(17,27)(18,23)(19,21)(22,34)(25,38)(28,40)(29,44)(30,43)(31,41)(32,37)(33,35)(36,52)(39,54)(42,56)(45,60)(46,62)(47,63)(48,59)(49,57)(50,55)(51,53)(58,70)(61,72)(64,74)(65,78)(66,77)(67,75)(68,73)(69,71)(76,84)(79,86)(80,88)(81,89)(82,87)(83,85)(90,94)(91,96)(92,97)(93,95)(98,100)(99,101)(103,105);(2,3,4,5)(6,9,10,11)(7,13,14,8)(12,19,20,21)(15,23,24,18)(16,17,26,27)(22,33,34,35)(25,37,38,32)(28,31,40,41)(29,43,44,30)(36,51,52,53)(39,55,54,50)(42,49,56,57)(45,59,60,48)(46,47,62,63)(58,69,70,71)(61,73,72,68)(64,67,74,75)(65,77,78,66)(76,83,84,85)(79,87,86,82)(80,81,88,89)(90,93,94,95)(91,97,96,92)(98,99,100,101)(102,103)(104,105)(106,107,109,113,110,112,116,119)(108,111,114,118,115,117,120,121)

Polycyclic presentation:

2^7,101|a^2=f,c^2=f,f^2=g,b^a=be,d^a=dg,h^a=h^91,h^b=h^100,h^c=h^10,h^f=h^100

Conjugacy classes & character table

406 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 21227);