C₇₉×#7267 #34118956

order	20224
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₄²×C₇₉ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₇₉×#7267

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#329
commutator	C₄²	C₄²×C₇₉
Frattini, cosocle	C₂×#97	C₂²×C₇₉
socle	C₂×C₇₉	#1295
prime radical	C₂³×C₇₉	#101
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#97×C₇₉ ◁ G

196 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 111
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 2 generators on 111 points:

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

Conjugacy classes & character table

3160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 255);