C₁₀₁×#11811 #38793962

order	25856
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₁ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₁×#11811

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₀₁
Frattini, cosocle	C₂×C₂²⋊C₄	C₂³×C₁₀₁
prime radical	C₂⁵×C₁₀₁	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂⁴×C₁₀₁ ◁ C₂²×C₂²⋊C₄×C₁₀₁ ◁ G

496 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 3232

A minimal faithful permutation representation — 3 generators on 133 points:

(1,2)(3,11,14,28)(4,16,19,9)(5,8)(6,10)(7,13,22,17)(12,29,15,26)(18,25)(20,27,32,24)(21,31,23,30)(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)(2,7,10,23)(4,17)(5,15)(6,12)(8,22,25,21)(9,26,16,28)(11,27,29,24)(13,20)(14,18)(19,31)(30,32);(2,8)(3,12)(7,21)(9,24)(10,25)(11,28)(13,30)(14,15)(16,27)(17,31)(22,23)(26,29)

Conjugacy classes & character table

2828 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25856, 4799);