C₁₀₃×#13680 #39918955

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

Aliases

direct product

C₁₀₃×#13680

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₀₃	#2196
commutator, Frattini, cosocle	#124	C₂³×C₁₀₃
prime radical	C₁₀₃×#3289	C₂
LCS	G ▷ #124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₀₃ ◁ C₂²×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ #124×C₁₀₃ ◁ G

378 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 135
transitive degree	μ_t(G) = 3296

A minimal faithful permutation representation — 3 generators on 135 points:

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

Conjugacy classes & character table

2266 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 6668);