C₈₃×#7303 #35235127

order	21248
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄²×C₈₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈₃×#7303

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#340
commutator	C₂×C₈	C₄²×C₈₃
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₈₃
prime radical	C₂³×C₈₃	#103
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ C₂×C₄×C₈×C₈₃ ◁ G

204 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 123
transitive degree	μ_t(G) = 10624

A minimal faithful permutation representation — 2 generators on 123 points:

(1,2,5,7,6,3,4,8)(9,10,13,19,16,21,15,31)(11,22,24,37,26,38,29,33)(12,20,14,30,28,36,27,18)(17,25,32,23,35,39,34,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123);(1,3,6,2)(4,7,5,8)(9,11,14,25,13,29,28,40,16,26,27,39,15,24,12,23)(10,17,20,33,31,32,18,22,21,35,36,37,19,34,30,38)

Conjugacy classes & character table

3818 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 291);