C₇₉×#7452 #34119141

order	20224
nilpotency class	5
isoclinism	isoclinic class of #7418
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇₉×#7452

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₇₉	#357
commutator	C₂×C₁₆	C₂×C₄×C₇₉
Frattini, cosocle	C₄×C₁₆	C₂²×C₇₉
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₄²×C₇₉ ◁ C₄×C₈×C₇₉ ◁ C₄×C₁₆×C₇₉ ◁ G

102 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 102 conjugacy classes of subgroups — too many to draw. Only its 54 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 — 2 generators on 119 points:

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

Conjugacy classes & character table

3871 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 440);