C₈₃×#9837 #35237661

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂³×C₈

Aliases

direct product

C₈₃×#9837

Subgroups

	subgroup	G/H
center, socle	C₂³×C₈₃	#127
commutator	C₄²	C₂²×C₄×C₈₃
Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
prime radical	C₂×#493×C₈₃	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

710 conjugacy classes of subgroups; only the 214 normal subgroups are shown.

normal subgroups only

This group has 710 conjugacy classes of subgroups — too many to draw. Only its 214 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) = 103
transitive degree	μ_t(G) = 10624

A minimal faithful permutation representation — 3 generators on 103 points:

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

Conjugacy classes & character table

4316 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 2825);