C₇₉×#7393 #34119082

order	20224
nilpotency class	3
isoclinism	isoclinic class of #327
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₇₉×#7393

Subgroups

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

110 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 110 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 20224

A minimal faithful permutation representation — 2 generators on 119 points:

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

Conjugacy classes & character table

6004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 381);