C₇₉×#13713 #34125402

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₇₉×#13713

Subgroups

	subgroup	G/H
center, socle	C₂²×C₇₉	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₇₉
prime radical	C₇₉×#2215	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂²×C₈×C₇₉ ◁ C₂²×C₁₆×C₇₉ ◁ G

178 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 178 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 10112

A minimal faithful permutation representation — 3 generators on 119 points:

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

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, 6701);