C₁₀₁×#11752 #38793903

order	25856
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₁×#11752

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂²×C₈	C₂³×C₁₀₁
prime radical	C₂³×C₁₀₁	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ C₂×C₄×C₈×C₁₀₁ ◁ G

320 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 141
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 3 generators on 141 points:

(2,6,7,8)(9,10,13,18,15,19,14,29)(11,20,23,38,21,37,30,34)(12,24,26,35,28,36,27,17)(16,25,32,39,31,40,33,22)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141);(1,2)(3,6)(4,8)(5,7)(9,11,15,21)(10,16,19,31)(12,25,28,40)(13,23,14,30)(17,34,35,38)(18,32,29,33)(20,36,37,24)(22,26,39,27);(1,3,5,4)(2,6,7,8)(11,21)(16,31)(20,37)(22,39)(23,30)(25,40)(32,33)(34,38)

Conjugacy classes & character table

4646 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25856, 4740);