C₈₃×#9981 #35237805

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₈₃×#9981

Subgroups

	subgroup	G/H
center, socle	C₂²×C₈₃	#392
commutator, Frattini, cosocle	C₂³×C₄	C₂³×C₈₃
prime radical	C₈₃×#3006	C₂
LCS	G ▷ C₂³×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₃ ◁ C₂³×C₄×C₈₃ ◁ G

764 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 5312

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

(1,2)(3,5)(4,6)(7,8)(9,10,14,17)(11,18,20,23)(12,22,13,16)(15,21,24,19)(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);(5,8)(9,11)(10,15)(12,21)(13,19)(14,20)(16,23)(17,24)(18,22);(1,3)(2,5)(4,7)(6,8)(11,19)(12,13)(15,23)(16,22)(18,24)(20,21)

Conjugacy classes & character table

2324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 2969);