C₁₀₁×#2016 #27167370

order	12928
nilpotency class	3
isoclinism	isoclinic class of #1999
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₁×#2016

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₀₁	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₁₀₁
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

370 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 3 generators on 125 points:

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

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₀₁×#7405, C₁₀₁×#7756, C₁₀₁×#7757, …
maximal normal subgroup of	C₁₀₁×#7405, C₁₀₁×#7756, C₁₀₁×#7757, …
maximal quotient of	C₁₀₁×#9957, C₁₀₁×#9959, C₁₀₁×#9967, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12928, 748);