C₇₉×#10511 #34122200

order	20224
nilpotency class	3
isoclinism	isoclinic class of #10508
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₇₉×#10511

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	#394
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₇₉
prime radical	C₂³×C₇₉	#121
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂×C₄²×C₇₉ ◁ G

338 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 94 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)(5,9)(8,13)(10,14)(11,16)(12,15)(17,18,22,27)(19,28,30,24)(20,26,21,25)(23,31,32,29)(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);(1,3,5,11)(2,6,9,16)(4,12,13,10)(7,15,8,14)(17,19)(18,23)(20,31)(21,29)(22,30)(24,25)(26,28)(27,32);(2,7)(4,13)(6,14)(8,9)(10,12)(15,16)(17,19,20,29,22,30,21,31)(18,24,25,23,27,28,26,32)

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, 3499);