C₁₀₁×#19711 #38801862

order	25856
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₁ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₀₁×#19711

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₁
prime radical	C₂³×C₁₀₁	#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₁ ◁ C₂×C₄²×C₁₀₁ ◁ G

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

normal subgroups only

This group has 636 conjugacy classes of subgroups — too many to draw. Only its 230 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) = 149
transitive degree	μ_t(G) = 12928

A minimal faithful permutation representation — 4 generators on 149 points:

(1,2)(3,10)(4,8)(5,14)(6,9)(7,13)(11,16)(12,15)(17,18,23,27)(19,28,32,43)(20,25,34,41)(21,26,22,36)(24,30,38,31)(29,42,45,47)(33,39,35,40)(37,46,48,44)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149);(3,11)(7,15)(10,16)(12,13)(17,19,21,30,23,32,22,31)(18,24,36,43,27,38,26,28)(20,29,35,46,34,45,33,44)(25,37,39,47,41,48,40,42);(1,3,5,13,6,11,4,12)(2,7,8,10,9,15,14,16)(17,20)(18,25)(19,29)(21,35)(22,33)(23,34)(24,37)(26,40)(27,41)(28,42)(30,46)(31,44)(32,45)(36,39)(38,48)(43,47);(1,4,6,5)(2,8,9,14)(3,12,11,13)(7,10,15,16)(17,21,23,22)(18,26,27,36)(19,30,32,31)(20,33,34,35)(24,28,38,43)(25,39,41,40)(29,44,45,46)(37,47,48,42)

Conjugacy classes & character table

4040 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25856, 12699);