C₁₀₃×#8478 #39913753

order	26368
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₃×#8478

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₃
prime radical	C₂×#41×C₁₀₃	C₂×C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 151
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 3 generators on 151 points:

(1,2,5,10,6,9,13,16)(3,8,11,15,4,7,12,14)(17,18)(19,27)(20,31,33,24)(21,34)(22,26)(23,29)(25,37)(28,43,45,48)(30,41)(32,40,36,42)(35,39)(38,44,47,46)(49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151);(1,3,6,4)(2,7,9,8)(5,12,13,11)(10,15,16,14)(17,19,22,30)(18,23,26,39)(20,28,33,45)(21,35,37,29)(24,38,31,47)(25,41,34,27)(32,46,36,44)(40,43,42,48);(1,4,6,3)(2,8,9,7)(5,11,13,12)(10,14,16,15)(17,20,22,33)(18,24,26,31)(19,28,30,45)(21,36,37,32)(23,38,39,47)(25,42,34,40)(27,43,41,48)(29,46,35,44)

Conjugacy classes & character table

4120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 1466);