C₈₃×#8477 #35236301

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₈₃×#8477

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#379
commutator	C₂²×C₄	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	#535×C₈₃	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

682 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 682 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 131
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 3 generators on 131 points:

(1,2,4,8,5,7,13,15)(3,9,10,16,11,6,12,14)(17,18)(19,27)(20,31,33,24)(21,34)(22,26)(23,29)(25,37)(28,43,45,48)(30,41)(32,40,36,42)(35,39)(38,44,47,46)(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);(1,3,5,11)(2,6,7,9)(4,12,13,10)(8,16,15,14)(17,19,22,30)(18,23,26,39)(20,28,33,45)(21,35,37,29)(24,38,31,47)(25,41,34,27)(32,46,36,44)(40,43,42,48);(2,7)(4,13)(6,9)(10,12)(17,20)(18,24)(19,28)(21,36)(22,33)(23,38)(25,42)(26,31)(27,43)(29,46)(30,45)(32,37)(34,40)(35,44)(39,47)(41,48)

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1465);