C₁₀₁×#7295 #38789446

order	25856
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₁ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₁×#7295

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	#340
commutator	C₂×C₈	C₄²×C₁₀₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₀₁
prime radical	C₂³×C₁₀₁	#107
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ C₂×C₄×C₈×C₁₀₁ ◁ G

188 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 133
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 2 generators on 133 points:

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

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, 283);