C₇₉×#13373 #34125062

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13373
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#13373

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#486
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
socle	C₂×C₇₉	#2023
prime radical	C₂×#135×C₇₉	C₂²
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×#97×C₇₉ ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 2528

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

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

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, 6361);