C₇₉×#9941 #34121630

order	20224
nilpotency class	3
isoclinism	isoclinic class of #9938
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#9941

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₇₉
prime radical	C₂×#121×C₇₉	C₂²
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂³×C₄×C₇₉ ◁ G

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

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 5056

A minimal faithful permutation representation — 3 generators on 111 points:

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

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, 2929);