#27170888

order	12928
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₄²

Aliases

No aliases for this group.

Splittings

Sylow

C₁₀₁ ⋊ #1747

Subgroups

	subgroup	G/H
center	C₄	C₄²×D₁₀₁
commutator	C₄×C₁₀₁	C₂×C₄²
Frattini	C₂²×C₄	C₂²×D₁₀₁
Fitting	#338×C₁₀₁	C₂
socle	C₂×C₁₀₁	#376
prime radical	C₂³×C₁₀₁	#41
cosocle	C₂²×C₄×C₁₀₁	C₂³
hypercenter	#338	D₁₀₁
hypocenter	C₁₀₁	#1747
LCS	G ▷ C₄×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄ ◁ #338

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 133
transitive degree	μ_t(G) = 3232

A minimal faithful permutation representation — 3 generators on 133 points:

(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(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)(102,105,106,116,107,117,118,129)(103,109,110,121,111,122,123,131)(104,113,114,126,115,127,128,133)(108,119,112,124,120,130,125,132);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(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)(100,101)(102,104)(103,108,111,120)(105,113)(106,114)(107,115)(109,119,122,130)(110,112,123,125)(116,126)(117,127)(118,128)(121,124,131,132)(129,133);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(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)(100,101)(102,103)(104,112,115,125)(105,109)(106,110)(107,111)(108,114,120,128)(113,124,127,132)(116,121)(117,122)(118,123)(119,126,130,133)(129,131)

Polycyclic presentation:

2^7,101|a^2=e,b^2=f,c^2=d,d^2=g,b^a=bd,f^a=fg,h^a=h^100,e^b=eg,h^b=h^100,h^c=h^100

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 4266);