C₁₀₃×#33821 #39939096

order	26368
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₀₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₀₃×#33821

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₁₀₃
prime radical	C₂³×C₁₀₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂×C₄²×C₁₀₃ ◁ C₂×C₄×C₈×C₁₀₃ ◁ G

484 conjugacy classes of subgroups; only the 202 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 202 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) = 13184

A minimal faithful permutation representation — 4 generators on 143 points:

(2,5)(3,7)(9,10,15,19)(11,16,14,30)(12,22,25,39)(13,26,29,38)(17,32,34,24)(18,21,36,28)(20,37,23,35)(27,31,40,33)(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);(1,2)(3,6)(4,5)(7,8)(9,11,15,14)(10,16,19,30)(12,23,25,20)(13,21,29,28)(17,33,34,31)(18,26,36,38)(22,35,39,37)(24,40,32,27);(2,5)(6,8)(9,12,15,25)(10,17,19,34)(11,20,14,23)(13,27,29,40)(16,31,30,33)(18,35,36,37)(21,32,28,24)(22,38,39,26);(1,3,4,7)(2,6,5,8)

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, 26809);