C₇₉×#13488 #34125177

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

Aliases

direct product

C₇₉×#13488

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	#481
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
prime radical	C₂³×C₇₉	C₂×SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#97×C₇₉ ◁ G

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

normal subgroups only

This group has 302 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) = 115
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 3 generators on 115 points:

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

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, 6476);