C₇₉×#13709 #34125398

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13709
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₉×#13709

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2226
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	#508×C₇₉	C₂²
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₄×C₈×C₇₉ ◁ C₄×C₁₆×C₇₉ ◁ G

154 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 143
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 143 points:

(1,2)(3,16)(4,22,26,56)(5,14)(6,28)(7,11)(8,15)(9,18)(10,24,38,51)(12,19)(13,20)(17,46,49,40)(21,35)(23,57,32,55)(25,60,47,54)(27,45)(29,43,59,33)(30,62)(31,34)(36,63,44,58)(37,48,64,61)(39,52)(41,50)(42,53)(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);(1,3,5,18,8,21,7,20)(2,9,11,16,15,13,14,35)(4,17,23,47,26,49,32,25)(6,19,27,50,31,53,30,52)(10,33,36,37,38,43,44,64)(12,34,39,45,42,28,41,62)(22,54,55,46,56,60,57,40)(24,48,58,29,51,61,63,59);(1,4)(2,10)(3,17)(5,23)(6,29)(7,32)(8,26)(9,33)(11,36)(12,40)(13,43)(14,44)(15,38)(16,37)(18,47)(19,51)(20,25)(21,49)(22,34)(24,53)(27,61)(28,56)(30,48)(31,59)(35,64)(39,54)(41,60)(42,46)(45,55)(50,63)(52,58)(57,62)

Conjugacy classes & character table

2923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6697);