C₇₉×#13660 #34125349

order	20224
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₉×#13660

Subgroups

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

158 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 158 conjugacy classes of subgroups — too many to draw. Only its 126 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:

(1,2,4,6)(3,7,8,5)(9,10,12,17,13,18,24,31,14,19,16,29,26,33,30,39,15,20,25,32,27,34,38,40,28,11,21,22,35,23,36,37)(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);(1,3,4,8)(2,5,6,7);(9,11,12,22,13,23,24,37,14,10,16,17,26,18,30,31,15,19,25,29,27,33,38,39,28,20,21,32,35,34,36,40)

Conjugacy classes & character table

8848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6648);