C₇₉×#13444 #34125133

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

Aliases

direct product

C₇₉×#13444

Subgroups

	subgroup	G/H
center	C₄×C₇₉	#469
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₉
socle	C₂×C₇₉	#2054
prime radical	C₇₉×#3414	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₇₉ ◁ C₂²×C₄×C₇₉ ◁ C₂×C₄×C₈×C₇₉ ◁ G

392 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 106 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)(3,14)(4,18)(5,22)(6,27)(7,13)(8,15)(9,19)(10,25)(11,29)(12,24)(16,21)(17,20)(23,32)(26,31)(28,30)(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)(2,8)(4,10)(5,23)(6,18)(7,17)(9,29)(11,21)(12,32)(13,19)(14,22)(15,25)(16,24)(20,31)(26,30)(27,28);(1,4,5,8,24,14,29,32,7,21,26,19,6,20,25,28)(2,9,10,16,27,23,31,3,13,15,11,18,12,30,22,17)

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, 6432);