C₇₉×#13309 #34124998

order	20224
nilpotency class	4
isoclinism	isoclinic class of #13309
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₇₉×#13309

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
socle	C₂×C₇₉	#1999
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂³×C₈×C₇₉ ◁ G

568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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)(3,11)(4,15)(5,20)(6,9)(7,12)(8,18)(10,17)(13,27)(14,29)(16,26)(19,30)(21,24)(22,28)(23,31)(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);(1,3)(2,7)(4,16)(5,21)(6,13)(8,24)(9,22)(10,26)(11,15)(12,18)(14,17)(19,31)(20,23)(25,29)(27,30)(28,32);(7,22)(11,27)(23,26)(24,29)

Conjugacy classes & character table

3160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 6297);