C₁₀₃×#8453 #39913728

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

Aliases

direct product

C₁₀₃×#8453

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₀₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₀₃
prime radical	C₁₀₃×#3484	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂³×C₄×C₁₀₃ ◁ G

1330 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1330 conjugacy classes of subgroups — too many to draw. Only its 158 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 — 3 generators on 119 points:

(2,6,8,14)(3,10)(7,11,9,15)(12,16)(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);(1,2)(3,11)(4,9)(5,7)(6,12)(8,13)(10,14)(15,16);(3,12)(6,11)(10,16)(14,15)

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, 1441);