C₇₉×#13487 #34125176

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13398
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#13487

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
prime radical	C₂²×D₈×C₇₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#97×C₇₉ ◁ G

338 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 99
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 99 points:

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

Conjugacy classes & character table

2686 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6475);