C₈₃×#8534 #35236358

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₈₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₈₃×#8534

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#379
commutator	C₂⁴	C₂²×C₄×C₈₃
Frattini, cosocle	C₂⁵	C₂³×C₈₃
prime radical	C₈₃×#3484	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂⁵×C₈₃ ◁ G

1408 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 99
transitive degree	μ_t(G) = 1328

A minimal faithful permutation representation — 3 generators on 99 points:

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

Conjugacy classes & character table

3320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1522);