C₇₉×#13671 #34125360

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13669
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#13671

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2184
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	C₇₉×#3415	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂×C₄×C₇₉ ◁ #131×C₇₉ ◁ #504×C₇₉ ◁ G

284 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 74 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:

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

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, 6659);