C₁₀₁×#13856 #38796007

order	25856
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₀₁×#13856

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₁₀₁	C₂³
commutator	C₂³	C₂³×C₄×C₁₀₁
Frattini, cosocle	C₂⁴	C₂⁴×C₁₀₁
socle, prime radical	C₂⁴×C₁₀₁	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₁₀₁ ◁ G

1774 conjugacy classes of subgroups; only the 734 normal subgroups are shown.

normal subgroups only

This group has 1774 conjugacy classes of subgroups — too many to draw. Only its 734 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) = 121
transitive degree	μ_t(G) = 25856

A minimal faithful permutation representation — 4 generators on 121 points:

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

Conjugacy classes & character table

8888 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25856, 6844);