C₇₉×#13678 #34125367

order	20224
nilpotency class	5
isoclinism	isoclinic class of #13677
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₇₉×#13678

Subgroups

	subgroup	G/H
center, socle	C₂×C₇₉	#2196
commutator, Frattini, cosocle	#124	C₂³×C₇₉
LCS	G ▷ #124 ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₇₉ ◁ C₂²×C₇₉ ◁ C₂×C₄×C₇₉ ◁ #124×C₇₉ ◁ G

400 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 58 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:

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

Conjugacy classes & character table

1738 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6666);