C₇₉×#7796 #34119485

order	20224
nilpotency class	3
isoclinism	isoclinic class of #7734
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₇₉×#7796

Subgroups

	subgroup	G/H
center, socle	C₂³×C₇₉	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
prime radical	C₇₉×#2733	C₂
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

478 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 10112

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

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

Conjugacy classes & character table

2923 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 784);