#27186047

order	12928
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆ · Schur multiplier (H₂) = C₄

Aliases

No aliases for this group.

Splittings

Sylow

C₁₀₁ ⋊ #1312

Subgroups

	subgroup	G/H
center, Frattini	C₄²	C₂×#87938
commutator	C₂×C₁₀₁	C₄×C₁₆
Fitting	C₄×C₈×C₁₀₁	C₄
socle, prime radical	C₂²×C₁₀₁	C₄×C₈
cosocle	C₄×#11717579	C₂²
hypercenter	C₄×C₈	#87938
hypocenter	C₁₀₁	#1312
LCS	G ▷ C₂×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₄² ◁ C₄×C₈

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 125
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 2 generators on 125 points:

(1,2,7,4)(3,11,14,9)(5,16,13,6)(8,24,23,18)(10,29,26,15)(12,20,27,22)(17,41,36,31)(19,46,43,28)(21,37,40,35)(25,33,44,39)(30,62,53,48)(32,65,49,45)(34,58,57,52)(38,54,61,56)(42,50,64,60)(47,80,68,63)(51,77,72,67)(55,73,76,71)(59,69,79,75)(66,91,83,78)(70,88,87,82)(74,84,90,86)(81,98,94,89)(85,95,97,93)(92,101,100,96)(103,106)(107,109)(110,111,112,115,113,116,118,121,114,117,119,122,120,123,124,125);(2,3)(4,6)(5,8)(7,12)(9,15)(10,17)(11,13)(14,21)(16,25)(18,28)(19,30)(20,26)(22,24)(23,34)(27,38)(29,42)(31,45)(32,47)(33,43)(35,41)(36,51)(37,39)(40,55)(44,59)(46,63)(48,65)(49,50)(52,62)(53,66)(54,60)(56,58)(57,70)(61,74)(64,78)(67,80)(68,69)(71,77)(72,81)(73,75)(76,85)(79,89)(82,91)(83,84)(86,88)(87,92)(90,96)(93,98)(94,95)(97,99)(100,101)(102,103,104,107,105,106,108,109)

Polycyclic presentation:

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

Conjugacy classes & character table

880 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 19425);