C₁₀₁×#7134 #38789285

order	25856
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₀₁ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₀₁×#7134

Subgroups

	subgroup	G/H
center	C₄×C₁₀₁	#333
commutator	C₄²	C₂×C₈×C₁₀₁
Frattini, cosocle	C₄³	C₂²×C₁₀₁
socle	C₂×C₁₀₁	#1272
prime radical	C₂³×C₁₀₁	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₁ ◁ C₂²×C₄×C₁₀₁ ◁ C₄³×C₁₀₁ ◁ G

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 117
transitive degree	μ_t(G) = 1616

A minimal faithful permutation representation — 2 generators on 117 points:

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

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, 122);