C₁₀₃×#13423 #39918698

order	26368
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#13423

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×D₄	C₂³×C₁₀₃
prime radical	C₂×#127×C₁₀₃	C₂²
LCS	G ▷ C₂²×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₂³×C₁₀₃ ◁ C₂²×D₄×C₁₀₃ ◁ G

558 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 123
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 3 generators on 123 points:

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

Conjugacy classes & character table

3193 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 6411);