C₁₀₃×#9759 #39915034

order	26368
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₀₃×#9759

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#390
commutator	C₄²	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₃
prime radical	C₂³×C₁₀₃	#127
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ G

370 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 6592

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

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

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, 2747);