C₁₀₃×#7492 #39912767

order	26368
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₀₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₀₃×#7492

Subgroups

	subgroup	G/H
center	C₄×C₁₀₃	AΣL(1,𝔽₁₆)
commutator	C₂×Q₈	C₄²×C₁₀₃
Frattini, cosocle	#532	C₂²×C₁₀₃
socle	C₂×C₁₀₃	#1390
prime radical	#532×C₁₀₃	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ #532×C₁₀₃ ◁ G

282 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 66 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) = 119
transitive degree	μ_t(G) = 1648

A minimal faithful permutation representation — 2 generators on 119 points:

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

Conjugacy classes & character table

3502 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 480);