C₇₉×#13450 #34125139

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#13450

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₉	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ C₂×C₄×C₈×C₇₉ ◁ G

410 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 119
transitive degree	μ_t(G) = 20224

A minimal faithful permutation representation — 3 generators on 119 points:

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

Conjugacy classes & character table

4108 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6438);