C₇₉×#7406 #34119095

order	20224
nilpotency class	5
isoclinism	isoclinic class of #7396
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#7406

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#353
commutator	C₂×M₁₆	C₂×C₄×C₇₉
Frattini, cosocle	#408	C₂²×C₇₉
socle	C₂×C₇₉	#1343
prime radical	C₇₉×#2017	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂×C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ #408×C₇₉ ◁ G

244 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 143 points:

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

Conjugacy classes & character table

2449 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 394);