C₁₀₃×#8539 #39913814

order	26368
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₀₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₀₃×#8539

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#379
commutator	C₂⁴	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₃
prime radical	C₁₀₃×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂³×C₄×C₁₀₃ ◁ G

1008 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1008 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) = 143
transitive degree	μ_t(G) = 6592

A minimal faithful permutation representation — 3 generators on 143 points:

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

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, 1527);