C₈₃×#7735 #35235559

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₈₃×#7735

Subgroups

	subgroup	G/H
center, socle	C₂³×C₈₃	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₈₃×#2011	C₂
LCS	G ▷ C₂×C₄² ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

604 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 107
transitive degree	μ_t(G) = 10624

A minimal faithful permutation representation — 3 generators on 107 points:

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

Conjugacy classes & character table

3071 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 723);