C₁₀₃×#13685 #39918960

order	26368
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₀₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₀₃×#13685

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₀₃	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₀₃
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₃ ◁ C₄²×C₁₀₃ ◁ C₄×C₈×C₁₀₃ ◁ C₄×C₁₆×C₁₀₃ ◁ G

232 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 139
transitive degree	μ_t(G) = 13184

A minimal faithful permutation representation — 3 generators on 139 points:

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

Conjugacy classes & character table

5047 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 6673);