C₁₀₃×#7360 #39912635

order	26368
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₀₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₀₃×#7360

Subgroups

	subgroup	G/H
center	C₄×C₁₀₃	#354
commutator	C₄²	C₂×C₈×C₁₀₃
Frattini, cosocle	#423	C₂²×C₁₀₃
socle	C₂×C₁₀₃	#1319
prime radical	C₂³×C₁₀₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₃ ◁ C₂×C₄×C₁₀₃ ◁ C₂²×C₄×C₁₀₃ ◁ #423×C₁₀₃ ◁ G

164 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 135 points:

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

Conjugacy classes & character table

2884 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26368, 348);