C₈₃×#10689 #35238513

order	21248
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₈₃×#10689

Subgroups

	subgroup	G/H
center	C₂×C₄×C₈₃	#124
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₈₃
socle	C₂²×C₈₃	#400
prime radical	C₂³×C₈₃	C₂²⋊Q₈
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₃ ◁ C₂×C₄²×C₈₃ ◁ G

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

normal subgroups only

This group has 248 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:

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

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, 3677);