C₈₃×#12684 #35240508

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₈₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₈₃×#12684

Subgroups

	subgroup	G/H
center	C₈×C₈₃	#120
commutator	C₂³	C₂²×C₈×C₈₃
Frattini, cosocle	C₂²×C₈	C₂³×C₈₃
socle	C₂×C₈₃	#1779
prime radical	#585×C₈₃	C₄
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₈₃ ◁ C₂²×C₈×C₈₃ ◁ G

894 conjugacy classes of subgroups; only the 210 normal subgroups are shown.

normal subgroups only

This group has 894 conjugacy classes of subgroups — too many to draw. Only its 210 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) = 147
transitive degree	μ_t(G) = 5312

A minimal faithful permutation representation — 3 generators on 147 points:

(1,2,5,10,6,11,20,30,7,12,21,31,22,32,43,53)(3,8,15,25,16,26,39,49,14,24,37,47,38,48,58,62)(4,9,18,28,19,29,42,52,17,27,40,50,41,51,59,63)(13,33,35,54,36,55,57,64,34,23,44,45,56,46,60,61)(65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147);(1,3)(2,8)(4,13)(5,15)(6,16)(7,14)(9,23)(10,25)(11,26)(12,24)(17,34)(18,35)(19,36)(20,39)(21,37)(22,38)(27,33)(28,45)(29,46)(30,49)(31,47)(32,48)(40,44)(41,56)(42,57)(43,58)(50,54)(51,55)(52,61)(53,62)(59,60)(63,64);(1,4)(2,9)(3,13)(5,18)(6,19)(7,17)(8,23)(10,28)(11,29)(12,27)(14,34)(15,35)(16,36)(20,42)(21,40)(22,41)(24,33)(25,45)(26,46)(30,52)(31,50)(32,51)(37,44)(38,56)(39,57)(43,59)(47,54)(48,55)(49,61)(53,63)(58,60)(62,64)

Conjugacy classes & character table

5312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 5672);